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Risk Simulation in Banking

2021-01-20T18:21:20Z

Simon: /* Bailouts: */

=Risk Simulation in Banking=

==Problem==
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

==Approach==

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

==Method==
Since the non-spatial nature of the problem, I chose to run a Monte Carlo Simulation. I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

==Detailed description==

There are basically two ways a bank can go bankrupt:

===Bank runs:===
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of its deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

===Asset Price Shock:===
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

===Bailouts:===
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year. In reality However, there would obviously not be a fixed upper limit, but the number of bailouts would depend on the political will, the financial ability of a state and the size of the collapse.

==Results==

===Test 1: increasing bailout willingness:===
[[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

===Test 2: Increased Liquidity:===
[[File:Liquidity.png|600px|thumb|right|]] Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

===Test 3: Increasing Equity:===
[[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

===Test 4: Increasing Equity, Liquidity and the willingness to bail out:===
[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

==Conclusion==
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the one-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

Eventhough the difficulties with the effects of Equity and Liquidity on the default probability, for realistically chosen settings (Eq.=100%, Lq.=100%, max#bailouts=4) the model delivers a average default probability which is very close to the actual bank-default-probability in Germany in the past 20 years (about one per decade [1]).

=Code=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=Reference List=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf Deutsche Bank Balance Sheet]

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html DZ Bank Balance Sheet]

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/ kfw Balance Sheet]

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf Commerzbank Balance Sheet]

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf Hypo Balance Sheet]

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf BayernLB Balance Sheet]

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf ING Balance Sheet]

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf LBBW Balance Sheet]

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/ NordLB Balance Sheet]

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf NRWBank Balance Sheet]

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf deka Balance Sheet]

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf Rentenbank Balance Sheet]

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf dt.Pfandbriefbank Balance Sheet]

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf hcob Balance Sheet]

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf Apobank Balance Sheet]

[https://en.wikipedia.org/wiki/List_of_corporate_collapses_and_scandals list of corporate collapses [1]]

Risk Simulation in Banking

2021-01-20T18:15:58Z

Simon:

=Risk Simulation in Banking=

==Problem==
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

==Approach==

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

==Method==
Since the non-spatial nature of the problem, I chose to run a Monte Carlo Simulation. I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

==Detailed description==

There are basically two ways a bank can go bankrupt:

===Bank runs:===
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of its deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

===Asset Price Shock:===
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

===Bailouts:===
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

==Results==

===Test 1: increasing bailout willingness:===
[[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

===Test 2: Increased Liquidity:===
[[File:Liquidity.png|600px|thumb|right|]] Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

===Test 3: Increasing Equity:===
[[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

===Test 4: Increasing Equity, Liquidity and the willingness to bail out:===
[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

==Conclusion==
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the one-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

Eventhough the difficulties with the effects of Equity and Liquidity on the default probability, for realistically chosen settings (Eq.=100%, Lq.=100%, max#bailouts=4) the model delivers a average default probability which is very close to the actual bank-default-probability in Germany in the past 20 years (about one per decade [1]).

=Code=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=Reference List=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf Deutsche Bank Balance Sheet]

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html DZ Bank Balance Sheet]

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/ kfw Balance Sheet]

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf Commerzbank Balance Sheet]

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf Hypo Balance Sheet]

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf BayernLB Balance Sheet]

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf ING Balance Sheet]

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf LBBW Balance Sheet]

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/ NordLB Balance Sheet]

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf NRWBank Balance Sheet]

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf deka Balance Sheet]

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf Rentenbank Balance Sheet]

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf dt.Pfandbriefbank Balance Sheet]

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf hcob Balance Sheet]

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf Apobank Balance Sheet]

[https://en.wikipedia.org/wiki/List_of_corporate_collapses_and_scandals list of corporate collapses [1]]

WS 2020/2021

2021-01-20T15:53:15Z

Simon:

Semestral papers from winter term 2020/2021. Please, put here links to the pages with your paper. First you need to have your [[Assignments WS 2020/2021|assignment approved]]

[http://www.simulace.info/index.php/Impact_of_late_lockdown_and_hospital_capacity_on_19-COVID_spread Impact of late lockdown and hospital capacity on 19-COVID spread] , Thomas BAEUMLIN [[User:Toscool|Toscool]] ([[User talk:Toscool|talk]]) 16:15, 7 January 2020 (CET)

[[Comparing_multiple_airplane_boarding_methods]], Adam Jedlička [[User:Jeda00|jeda00]] 20:45, 17 January 2020 (CET)

[http://www.simulace.info/index.php/Effects_of_VAT_exemption_abolition_to_imported_low_value_consignments Effects of VAT exemption abolition to imported low value consignments], Adela Barchankova [[User:bara15|bara15]] ([[User talk:bara15|talk]]) 21:00, 18 January 2020 (CET)

[[Retirement Planning]], [[User:Louis|Louis]] ([[User talk:Louis|talk]]) 02:08, 19 January 2021 (CET)

[[Covid 19 - Contacts]], [[User:praa03|praa03]] 17:08, 19 January 2021 (CET)

[[Corrupted Blood Incident]], [[User:Frym06|Frym06]] ([[User talk:Frym06|talk]]) 19:32, 19 January 2021 (CET)

WIP [[Car acquisition]], [[Mico00|Mico00]] 19:59, 19 January 2021 (CET)

[[Widening the spread between rich and poor]], [[User:Sára|Sára]] 21:40, 19 January 2021 (CET)

[[Development of real estate prices in Prague]], [[User:netp02|netp02]] 23:41, 19 January 2021 (CET)

[[IT Team simulation]], [[Antonsverlov]] , 20 January 2021 (CET)

[[Evolution of retirement pay in the Czech Republic]], Arnošt Sychra [[User:Syca00|Syca00]] 03:30, 20 January 2020 (CET)

[http://www.simulace.info/index.php/COVID-19_symptoms COVID-19 symptoms simulation] , Kamila Steinbartová [[User:stek15|stek15]] ([[User talk:stek15|talk]]) 13:07, 20 January 2020 (CET)

[http://www.simulace.info/index.php/Risk_Simulation_in_Banking Risk Simulation in Banking], Simon Orlik [[User:Simon|Simon]] ([[User talk:Simon|talk]]) 16:52, 20 January (CET)

Risk Simulation in Banking

2021-01-20T15:45:22Z

Simon:

=Risk Simulation in Banking:=

==Problem:==
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

==Approach:==

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

==Method:==
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

==Detailed description:==

There are basically two ways a bank can go bankrupt:

===Bank runs:===
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

===Asset Price Shock:===
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

===Bailouts:===
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

==Results:==

===Test 1: increasing bailout willingness:===
[[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

===Test 2: Increased Liquidity:===
[[File:Liquidity.png|600px|thumb|right|]] Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

===Test 3: Increasing Equity:===
[[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

===Test 4: Increasing Equity, Liquidity and the willingness to bail out:===
[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

==Conclusion:==
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

=Code:=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=References:=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf] Deutsche Bank Balance Sheet

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html] DZ Bank Balance Sheet

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/] kfw Balance Sheet

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf] Commerzbank Balance Sheet

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf] Hypo Balance Sheet

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf] BayernLB Balance Sheet

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf] ING Balance Sheet

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf] LBBW Balance Sheet

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/] NordLB Balance Sheet

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf] NRWBank Balance Sheet

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf] deka Balance Sheet

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf] Rentenbank Balance Sheet

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf] dt.Pfandbriefbank Balance Sheet

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf] hcob Balance Sheet

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf] Apobank Balance Sheet

Risk Simulation in Banking

2021-01-20T15:44:41Z

Simon: /* Conclusion: */

Risk Simulation in Banking

2021-01-20T15:43:15Z

Simon:

Risk Simulation in Banking

2021-01-20T15:42:07Z

Simon:

=Risk Simulation in Banking=

==Problem:==
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

==Approach:==

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

==Method:==
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

==Detailed description:==

There are basically two ways a bank can go bankrupt:

===Bank runs:===
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

===Asset Price Shock:===
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

===Bailouts:===
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

==Results:==

===Test 1: increasing bailout willingness:===
[[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

===Test 2: Increased Liquidity:===
[[File:Liquidity.png|600px|thumb|right|]] Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

===Test 3: Increasing Equity:===
[[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] ===Test 4: Increasing Equity, Liquidity and the willingness to bail out:=== In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

==Conclusion:==
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

=Code:=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=References:=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf] Deutsche Bank Balance Sheet

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html] DZ Bank Balance Sheet

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/] kfw Balance Sheet

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf] Commerzbank Balance Sheet

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf] Hypo Balance Sheet

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf] BayernLB Balance Sheet

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf] ING Balance Sheet

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf] LBBW Balance Sheet

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/] NordLB Balance Sheet

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf] NRWBank Balance Sheet

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf] deka Balance Sheet

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf] Rentenbank Balance Sheet

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf] dt.Pfandbriefbank Balance Sheet

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf] hcob Balance Sheet

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf] Apobank Balance Sheet

Risk Simulation in Banking

2021-01-20T15:39:58Z

Simon: /* Results: */

=Risk Simulation in Banking=

==Problem:==
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

==Approach:==

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

==Method:==
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

==Detailed description:==

There are basically two ways a bank can go bankrupt:

===Bank runs:===
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

===Asset Price Shock:===
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

===Bailouts:===
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

==Results:==

===Test 1: increasing bailout willingness:=== [[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

[[File:Liquidity.png|600px|thumb|right|]] ===Test 2: Increased Liquidity:=== Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

[[File:Equity.png|600px|thumb|right|]] ===Test 3: Increasing Equity:=== I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] ===Test 4: Increasing Equity, Liquidity and the willingness to bail out:=== In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

==Conclusion:==
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

=Code:=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=References:=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf] Deutsche Bank Balance Sheet

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html] DZ Bank Balance Sheet

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/] kfw Balance Sheet

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf] Commerzbank Balance Sheet

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf] Hypo Balance Sheet

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf] BayernLB Balance Sheet

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf] ING Balance Sheet

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf] LBBW Balance Sheet

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/] NordLB Balance Sheet

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf] NRWBank Balance Sheet

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf] deka Balance Sheet

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf] Rentenbank Balance Sheet

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf] dt.Pfandbriefbank Balance Sheet

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf] hcob Balance Sheet

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf] Apobank Balance Sheet

Risk Simulation in Banking

2021-01-20T15:33:10Z

Simon:

=Risk Simulation in Banking=

==Problem:==
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

==Approach:==

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

==Method:==
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

==Detailed description:==

There are basically two ways a bank can go bankrupt:

===Bank runs:===
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

===Asset Price Shock:===
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

===Bailouts:===
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

==Results:==

[[File:Bailouts.png|600px|thumb|right|]] =Test 1: increasing bailout willingness:= The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

[[File:Liquidity.png|600px|thumb|right|]] =Test 2: Increased Liquidity:= Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

[[File:Equity.png|600px|thumb|right|]] =Test 3: Increasing Equity:= I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] =Test 4: Increasing Equity, Liquidity and the willingness to bail out:= In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

==Conclusion:==
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

=Code:=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=References:=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf] Deutsche Bank Balance Sheet

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html] DZ Bank Balance Sheet

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/] kfw Balance Sheet

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf] Commerzbank Balance Sheet

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf] Hypo Balance Sheet

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf] BayernLB Balance Sheet

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf] ING Balance Sheet

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf] LBBW Balance Sheet

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/] NordLB Balance Sheet

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf] NRWBank Balance Sheet

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf] deka Balance Sheet

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf] Rentenbank Balance Sheet

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf] dt.Pfandbriefbank Balance Sheet

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf] hcob Balance Sheet

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf] Apobank Balance Sheet

Risk Simulation in Banking

2021-01-20T15:17:41Z

Simon: /* References: */

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

=Detailed description:=

There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

=Results:=

[[File:Bailouts.png|600px|thumb|right|]]'''Test 1: increasing bailout willingness:''' The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

[[File:Liquidity.png|600px|thumb|right|]]'''Test 2: Increased Liquidity:''' Secondly, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

[[File:Equity.png|600px|thumb|right|]]'''Test 3: Increasing Equity:''' I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]]'''Test 4: Increasing Equity, Liquidity and the willingness to bail out:''' In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

=Conclusion:=
[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default (picture on the right).

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

=Code:=
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

=References:=
[https://www.db.com/ir/de/download/Deutsche_Bank_Geschaeftsbericht_2018.pdf] Deutsche Bank Balance Sheet

[https://www.dzbank.de/content/dzbank_de/de/home/unser_profil/investorrelations/berichte/2018.html] DZ Bank Balance Sheet

[https://www.kfw.de/KfW-Konzern/%C3%9Cber-die-KfW/Berichtsportal/Gesch%C3%A4ftsbericht/Archiv/2018/Zahlen-und-Fakten/] kfw Balance Sheet

[https://www.commerzbank.de/media/aktionaere/service/archive/konzern/2019_1/Geschaeftsbericht_2018_Konzern_DE.pdf] Commerzbank Balance Sheet

[https://www.hypovereinsbank.de/content/dam/hypovereinsbank/ueber-uns/pdf/investor-relations/Berichte/DE/2019/Geschaeftsbericht-HVB-Group-2018.pdf] Hypo Balance Sheet

[https://www.bayernlb.de/internet/media/de/ir/downloads_1/investor_relations_3/finanzberichte/2018_21/Internet_Konzernabschluss_2018.pdf] BayernLB Balance Sheet

[https://www.ing.de/binaries/content/assets/pdf/ueber-uns/presse/publikationen/geschaftsbericht-2018-der-ing-holding-deutschland-gmbh.pdf] ING Balance Sheet

[https://www.lbbw.de/konzern/news-and-services/finanzberichte/geschaeftsberichte/2018/lbbw_geschaeftsbericht_2018_89rj14f1q_m.pdf] LBBW Balance Sheet

[https://www.nordlb.de/die-nordlb/ueber-uns/konzernzahlen/] NordLB Balance Sheet

[https://www.nrwbank.de/export/sites/nrwbank/de/corporate/downloads/presse/publikationen/finanzpublikationen/Geschaeftsbericht-2018-Finanzbericht.pdf] NRWBank Balance Sheet

[https://www.deka.de/site/dekade_deka-gruppe_site/get/documents_E2071643585/dekade/medienpool_dekade/deka_gruppe/de/Dokumente/Investor%20Relations/Finanzpublikationen/Gesch%C3%A4ftsberichte/Gesch%C3%A4ftsbericht%202018.pdf] deka Balance Sheet

[https://www.rentenbank.de/dokumente/Geschaeftsbericht-2018-Deutsch.pdf] Rentenbank Balance Sheet

[https://www.pfandbriefbank.com/fileadmin/user_upload/downloads/investor_relations/reports/1903_pbb_GB18_FINAL_de.pdf] dt.Pfandbriefbank Balance Sheet

[https://www.hcob-bank.de/media/pdf_3/investorrelations/geschaeftsber/2018_4/gb2018/de_hcob_ifrs-konzern_geschaeftsbericht_2018.pdf] hcob Balance Sheet

[https://www.apobank.de/dam/jcr:a21ac04d-5727-4dfe-b642-7eb37794cab6/apobank-jahresfinanzbericht-2018.pdf] Apobank Balance Sheet

Risk Simulation in Banking

2021-01-20T14:59:47Z

Simon:

Risk Simulation in Banking

2021-01-20T14:58:45Z

Simon: /* Risk Simulation in Banking */

Risk Simulation in Banking

2021-01-20T14:46:46Z

Simon: /* Risk Simulation in Banking */

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

'''Detailed description:'''

There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

'''Results:'''

'''Test 1: increasing bailout willingness''' [[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

'''Test 2: Increased Liquidity''' [[File:Liquidity.png|600px|thumb|right|]] Second, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

'''Test 3: Increasing Equity''' [[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

'''Test 4: Increasing Equity, Liquidity and the willingness to bail out'''
[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

'''Conclusion:'''[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default.

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bailouts it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

'''Code:'''
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

Risk Simulation in Banking

2021-01-20T14:44:15Z

Simon:

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

'''Detailed description:'''

There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

'''Results:'''

'''Test 1: increasing bailout willingness''' [[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

'''Test 2: Increased Liquidity''' [[File:Liquidity.png|600px|thumb|right|]] Second, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

'''Test 3: Increasing Equity''' [[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

'''Test 4: Increasing Equity, Liquidity and the willingness to bail out'''
[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

'''Conclusion:'''[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%. Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default.

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bail outs it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

'''Code:'''
[[File:Risk_in_Banking_Simulation_V1.xlsx]]

File:Risk in Banking Simulation V1.xlsx

2021-01-20T14:41:25Z

Simon: Excel Monte Carlo Simulation to derive the efficiency of different banking regulation measures.

== Summary ==
Excel Monte Carlo Simulation to derive the efficiency of different banking regulation measures.

Risk Simulation in Banking

2021-01-20T14:36:03Z

Simon:

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

'''Detailed description:'''

There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

'''Results:'''

'''Test 1: increasing bailout willingness''' [[File:Bailouts.png|600px|thumb|right|]] The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2. The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

'''Test 2: Increased Liquidity''' [[File:Liquidity.png|600px|thumb|right|]] Second, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

'''Test 3: Increasing Equity''' [[File:Equity.png|600px|thumb|right|]] I tested which influence increasing Equity would have on the default probability.
Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

'''Test 4: Increasing Equity, Liquidity and the willingness to bail out'''
[[File:Bailouts, equity, liquidity.png|600px|thumb|right|]] In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

'''Conclusion:'''
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy number in 10 years by almost 50%.
Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default.[[File:Chain reaction vs bail out.PNG|400px|thumb|right|]]

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bail outs it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

File:Chain reaction vs bail out.PNG

2021-01-20T14:35:00Z

Simon:

Risk Simulation in Banking

2021-01-20T14:07:43Z

Simon:

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''

[[File:Regression Graph.png|200px|thumb|left|]]
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I
therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going
through their financial statements. With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total
Assets managed in the real market.

Total Assets = 3E+06x^(-1,389),
Equity = 154453x^(-1,43),
Deposits = 996993x^(-1,238),
Liquid Assets = 221117x^(-1,753)

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

'''Detailed description:'''

There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png|200px|thumb|left|]] I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png|200px|thumb|left|]] Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

'''Results:'''

'''Test 1.: increasing bailout willingness'''
The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2.

[[File:Bailouts.png]]

The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

'''Test 2.: Increased Liquidity'''
Second, I simulated the effect an increase in liquidity would have on the default probability.

[[File:Liquidity.png]]

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

'''Test 3: Increasing Equity'''
I tested which influence increasing Equity would have on the default probability.

[[File:Equity.png]]

Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

'''Test 4: Increasing Equity, Liquidity and the willingness to bail out'''
In the last testing sequence, I tested the impact of all three variables together.

[[File:Bailouts, equity, liquidity.png]]

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

'''Conclusion:'''
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy amount in 10 years by almost 50%.
Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default.

[[File:Bankruptcies.png]] [[File:Bankruptcies2.png]]

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bail outs it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

Risk Simulation in Banking

2021-01-20T13:47:21Z

Simon:

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going through their financial statements.

[[File:Regression Graph.png]]

Total Assets = 3E+06x^(-1,389)
Equity = 154453x^(-1,43)
Deposits = 996993x^(-1,238)
Liquid Assets = 221117x^(-1,753)

With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total Assets managed in the real market.

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

'''Detailed description:'''
There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

[[File:Bank run.png]]

I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.

[[File:Asset price shock.png]]

Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

'''Results:'''
'''Test 1.: increasing bailout willingness'''
The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2.

[[File:Bailouts.png]]

The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

'''Test 2.: Increased Liquidity'''
Second, I simulated the effect an increase in liquidity would have on the default probability.

[[File:Liquidity.png]]

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

'''Test 3: Increasing Equity'''
I tested which influence increasing Equity would have on the default probability.

[[File:Equity.png]]

Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

'''Test 4: Increasing Equity, Liquidity and the willingness to bail out'''
In the last testing sequence, I tested the impact of all three variables together.

[[File:Bailouts, equity, liquidity.png]]

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

'''Conclusion:'''
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy amount in 10 years by almost 50%.
Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default.

[[File:Bankruptcies.png]] [[File:Bankruptcies2.png]]

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bail outs it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

File:Bankruptcies2.png

2021-01-20T13:45:54Z

Simon:

File:Bankruptcies.png

2021-01-20T13:45:32Z

Simon:

File:Bailouts, equity, liquidity.png

2021-01-20T13:44:30Z

Simon:

File:Equity.png

2021-01-20T13:43:45Z

Simon:

File:Liquidity.png

2021-01-20T13:42:44Z

Simon:

File:Bailouts.png

2021-01-20T13:41:47Z

Simon:

File:Asset price shock.png

2021-01-20T13:40:41Z

Simon:

File:Bank run.png

2021-01-20T13:39:46Z

Simon:

File:Regression Graph.png

2021-01-20T13:36:36Z

Simon: Simon uploaded a new version of File:Regression Graph.png

File:Regression Graph.png

2021-01-20T13:21:54Z

Simon:

Risk Simulation in Banking

2021-01-20T13:19:50Z

Simon: Created page with " == Risk Simulation in Banking == '''Problem:''' Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, t..."

== Risk Simulation in Banking ==

'''Problem:'''
Modern Banking is a highly volatile business with interdependencies not only to other banks, but to the economy as a whole, too. It is therefore that most of the economic crisis of the past century had been accelerated or caused entirely by the financial sector.
Because of the interdependencies and to avoid snowball effects when one financial institute tumbles, regulators began to introduce different sorts of safety mechanisms.
My goal is, to simulate the German banking market and deduct default probabilities with varying extends of banking regulation in place.

'''Approach:'''
Since there is no freely available data on the in-dept structure of the whole German banking market, the best approach is to simulate the environment based on samples. I therefore picked the 18 largest in Germany operating banks together with several smaller ones and fitted a regression on the variables determining a banks bankruptcy.
Most interesting for stress-testing a bank is its balance sheet fundamentals. I chose to simulate the total Assets, Equity, Deposits and liquid Assets which I acquired by going through their financial statements.

Total Assets = 3E+06x^(-1,389)
Equity = 154453x^(-1,43)
Deposits = 996993x^(-1,238)
Liquid Assets = 221117x^(-1,753)

With the fitted regression functions, I proceeded to project fictional banks to the point where total Assets on average equaled the total Assets managed in the real market.

'''Method:'''
I simulated geometric Brownian motions with a uniformly distributed multiplicator of m ϵ [0.8; 1.2] over 10 years for three of my four variables to represent the natural fluctuation of capital. The range for the multiplicator was arbitrarily set and could be specified further by a regression of the yearly change of the balance sheet information. Estimating the actual volatility of the yearly changes of the variables and introducing this information into the model would significantly increase the validity of the simulation.

'''Detailed description:'''
There are basically two ways a bank can go bankrupt:

'''Bank runs:'''
The first one is called a bank run. When customers lose trust in their bank, they might go and grab their deposits in order to save their money. Since the concept of fractional-reserve banking requires banks to only hold a share of it’s deposits as liquid cash, too many people collecting their deposits can dry up liquidity. The bank is forced to quickly sell their assets (even under their market value) to pay out their deposits. Once there is no more liquidity, the bank will need to file bankruptcy.

I will simulate this by giving the bank run a possibility of 1/5000 to happen to a bank in year 0. If there is a bank run, a uniformly distributed portion between [0:x] of deposits will be deducted from the concerned banks liquid Assets. The ‘x’ can be specified on the ‘Overview’ sheet as ‘Deposit outflow (bank runs, upper limit)’ to vary the percentage of deposits withdrawn.
If the liquidity is not sufficient to cover the extent of the bank run, the bank goes bankrupt.
Every bankrupt bank increases the probability of another bank getting a bank run by 1% since customers do not trust their deposits safety anymore. This is, to simulate the possibility of a Snowball effect where healthy banks get bank runs because of panics in the overall sector.
One can vary the initial amount of liquidity in year 0 by changing the ‘Liquidity multiplicator’ on the ‘Overview’ sheet to experiment with the effect, different liquidity levels do have on the bankruptcy chance.

'''Asset Price Shock:'''
The other main way for a bank to become bust is due to shocks to asset prices. If prices of the financial assets of the bank deflate while the deposits values are contractually fixed, the equity needs to decrease in order to balance out the financial statement. Once the asset prices dragged the equity to zero, bankruptcy is almost inevitable.
Same as bank runs, asset depreciation rarely concerns just one bank. Usually banks invest in a similar asset basket and market selloffs hit all of them in a comparable way. Therefore, the same chances of 1/5000 at t=0, with an increase of 1% for every bankrupt bank is put in place here too.
The real-world solution for fluctuating asset prices in banking is hedging. If the introduction of hedging is done right, the total asset position can be kept relatively stable since decreases in some assets are balanced out by increases in the value of the hedging instruments.
The way I modeled this is by introducing variable upper and lower limits for the asset price change in one given year. They too, can be found on the ‘Overview’ sheet.
Another method used for reducing the risk of asset price fluctuations is the increase of Equity. Similar to what I did with the liquidity, one can change the initial level of Equity on the ‘Overview’ sheet by changing the ‘Equity multiplicator’.

'''Bailouts:'''
Due to the risk of snowball effects, Governments oftentimes intervene when they see the danger of a financial institutions going insolvent. Therefore, I modeled a bailout option where one can put the maximum number of bailouts per year.

'''Results:'''
'''Test 1.: increasing bailout willingness'''
The first simulation run was done using a Liquidity-, and Equity multiplicator of 1, a uniformly distributed interval of ϵ [0; 0.5] for the deposit outflows and an interval of ϵ [0.8; 1.2] for the Brownian motion. The maximum number of bailouts per year was initially set to 0.
Each setting, I run 50 times, with one run simulating 10 years, giving a sample size of 500 bank years per setting. After that, the number of possible bailouts was increased by 2.

The willingness to bail out struggling financial institutions does have a significant influence both on the expected number of defaults same as on the standard deviation. With a maximum of 4 bailouts, the probability for a default nearly halves from 1,98 to 1 per 10-year interval, while standard deviation decreased from 3,09 to 1,60.

'''Test 2.: Increased Liquidity'''
Second, I simulated the effect an increase in liquidity would have on the default probability.

Not surprisingly, an increased liquidity reduced the average default probability and its standard deviation. However, the results have not been as robust as in the case of the bailouts.
This might be due to limitations in the model: While I assumed that in the case of a bank run a uniformly distributed amount of ϵ [0; 0.5] of deposits gets liquidated immediately, most of the deposits a bank has are contractually fixed to be paid out only after a cancelation period of anywhere between 1 week to 3 months, giving the banks enough time to organize a adequate amount of cash.
Also, in the European Union, there is a deposit insurance, guaranteeing 100.000€ per customer per institution in case of insolvencies, which additionally reduces the chances of bank runs and liquidity squeezes.
Therefore, financial institutions require fewer liquid assets than my model would suggest. Which led to an overestimate of the default probability caused by a seemingly lack of liquidity.

'''Test 3: Increasing Equity'''
I tested which influence increasing Equity would have on the default probability.

Same as in the case of Liquidity, the results show a slight decrease in default probability for increasing Equity. However, for an increase in Equity by 100%, one would expect a more extreme decrease in the average number of bankruptcies.

'''Test 4: Increasing Equity, Liquidity and the willingness to bail out'''
In the last testing sequence, I tested the impact of all three variables together.

Again, one is able to observe significant reductions in the average default probability. After the first three tests it seems likely that the effect is dominated by the willingness to bail out, which appears to be the single biggest influencer when it comes to reducing the number of bankruptcies in the model.

'''Conclusion:'''
Within the limitations of the model, bailing out struggling institutions seems to be the most promising way of government intervention when it comes to reducing the likeliness of a financial crisis. An increase in the maximum allowed number of bail outs from 0 to 4 reduced the average bankruptcy amount in 10 years by almost 50%.
Note that an increased willingness to bail out does not have a direct effect on the base probability for bankruptcies. However, bailed out institutions are not able to kick off a chain reaction of bankruptcies and therefore reduce the overall probability of default.

When it comes to Equity and Liquidity increases, the results are not that clear. In theory, both should reduce the default probability greatly while the model only showed small effects.
One reason for this is of course that real institutions are not static. When they realize the market environment is changing and becoming more risky, it is good practice to stock up on Liquidity. An Effect which is not visible in the year-to-year balance sheet information and therefore did not find its way into the model.
Also, as mentioned before, the Liabilities in form of customer deposits usually need to be canceled first before they can be accessed by the depositor. A more sophisticated model for bank runs should include a concept like Duration to model the in- and outflow of liquidity in a more realistic, day-to-day way.
It is for these two reasons that the Liquidity and Equity Quotas I observed in the balance sheet information seem to be too low for effectively reducing default risks in my model. However, thinking about the incentive problems that come with bail outs it would not be advisable to only rely on the tool of government money for avoiding a financial crisis.

Assignments WS 2020/2021

2020-12-19T13:17:50Z

Simon:

{{Ambox
| text = <div>
Please, put here your assignments. Do not forget to sign them. You can use <nowiki>~~~~</nowiki> (four tildas) for an automatic signature. Use Show preview in order to check the result before your final sumbition.
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{{Ambox
| text = <div>
Please, strive to formulate your assignment carefully. We expect an adequate effort to formulate the assignment as it is your semestral paper. Do not forget that your main goal is a research paper. It means your simulation model must generate the results that are specific, measurable and verifiable. Think twice how you will develop your model, which entities you will use, draw a model diagram, consider what you will measure. No sooner than when you have a good idea about the model, submit your assignment. And of course, read [[How to deal with the simulation assignment|How to deal with the simulation assignment]].
</div>
}}

{{Ambox
| text = <div>
Topics on gambling, cards, etc. are not welcome.
</div>
}}

{{Ambox
| type = content
| text = <div>
In order to avoid possible confusion, please, check if you have added '''approved''' in bold somewhere in our comment under your submission. If there is no '''approved''', it means the assignment was not approved yet.
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}}

== Spread of 19-COVID ==
'''Author''' : [[User:Toscool|Toscool]] ([[User talk:Toscool|talk]]) 11:32, 11 December 2020 (CET)

'''Simulation''' : I will build a dynamic model of an epidemic his the dynamic issues. I will focus on the spread of Covid-19 in a population and Specially I will try to modelize the effect of a lockdown on the number of infections and deaths.
I will start with a susceptible population, with one infected people that infect 10 people with a certain probability. When you are infected you go the doctors and with a certain probability you go in the recovery population or in the hospital. Then you have a percentage of chance to die in this hospital or to recover. The lockdown will triggered when the ratio of people who where to the doctor and total population exceed a certain percentage. We lockdown and by reducing the number of people you infect in the beginning.

'''Goal of simulation''' : I aim to model the impact of a lockdown on the spread of COVID on a population. It will also show the difference between countries, for example if we lockdown too late. What will be the impact of these decisions.

'''Method''' : I will use VensimPLE for this simulation, as it is a dynamic system, and In my home university I know that I will need to use VensimPLE for a future project and course so it will help me a lot.

::The topic souds good - the question is, on what data sources will you base your simulation (equations) on? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 22:13, 12 December 2020 (CET)
:::I will use the case of Switzerland and use data from this website (https://corona-data.ch). I will try to reproduce the number of cases and the speed of the spread.[[User:Toscool|Toscool]] ([[User talk:Toscool|talk]]) 13:39, 13 December 2020 (CET)
::: OK. '''Approved''' but do not forget to include in the report for the simulation how you have derived the equations in the simulation from the data. [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 22:49, 14 December 2020 (CET)

== NFL Free Agency ==
'''Author''' : [[User:TimWalenczak|TimWalenczak]] ([[User talk:TimWalenczak|talk]]) 14:14, 18 December 2020 (CET)

'''Simulation''' : Free agency is a period during the off-season in the National Football League in the US. During that period, all 32 teams in the league can sign active players that have no contract with any other team, so-called free agents. The process goes as follows: at the beginning of free agency a certain amount of players become free agents due to expiring contracts. All players belong to one out of 8 position groups and want to receive a certain salary. Their starting position on the simulation grid is randomly assigned and they will move over the grid. The overall number of free agents is defined manually while they are randomly distributed over all position groups, as well as their desired salary, which is within a certain manually defined range. Whereas all the teams are looking for players from certain position groups and have a certain amount of money they can spend on them. The teams have fixed positions on the grid and do not move during the simulation. The maximum number of players a team is looking for is defined manually, while the desired position group is defined randomly from the list of position groups and the money to spend is randomly distributed over a certain manually defined salary range. When the simulation starts, the initial demand and supply ratio of a specific position is calculated and affects a player’s value. This means a player’s desired salary rises or decreases due to that demand and supply ratio. During the simulation players move over the grid. Players and teams get in touch when they are located next to each other. When a team’s position group needs matches the player’s position group and a player’s salary fits the money a team offers, the team signs this player and he disappears from the free agency market (turtle dies). If the offer doesn’t fit the need, a player walks on to the next team (turtle takes a random angle turn and walks until it approaches another team). Each team can negotiate only with one player at a time, and vice versa. With every round/tick/signing the demand and supply ratio is recalculated and the desired salary of all players in each position group changes and so does the amount of money teams are able to spend on further players (assuming they just signed a player). Free agency ends after a distinct number of ticks or even earlier if there are no more players left or teams do not have any money left to spend.

'''Goal of simulation''' : is to find out how a player’s value changes during the period of free agency. Especially interesting is, whether players that sign a new contract early in the period received higher payments or the ones signing late in the period. Maybe a certain strategy can be deducted for players depending on their initial demand and supply ratio in order to reach a highly paid contract.

'''Method''' : Since I don’t know VensimPLE yet, I think I will use NetLogo, because I see some similarities between my case and the “Market Structure” case we modelled recently.

: It is a bit unusual, but I can see something in common rather with Market Structure than with Building Escape. Please, just elaborate it into a greater detail and specify, how exactly should your simulation work. I am not sure you have a coherent idea about the solution. But if you work this out, I don't see a problem. [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 21:45, 11 December 2020 (CET)

: Yeah you are right I meant the Market Structure, sorry for the confusion! Okay, I updated the description above trying to go more into details. [[User:TimWalenczak|TimWalenczak]] ([[User talk:TimWalenczak|talk]]) 14:14, 18 December 2020 (CET)

==COVID-19 mass testing==

'''Author''' : [[User:Milan P|Milan P]] ([[User talk:MilanP|talk]]) 20:15, 13 December 2020 (CET)

'''Simulation''' : I will create simulation for mass Covid-19 testing in Slovakian village or small city. In previous rounds of this real mass testing in Slovakia testing itself took place in one day and in one sampling point, this will be the same with this simulation. In this model roles (medical staff, administrative workers, and police officer), will have assigned costs to them in order to include financial aspect into the simulation. Duration of the simulation will be 4 hours. This will serve as base model which will be adjusted in two ways. Firstly, I will create another model in which I will duplicate sampling point so 2 sampling points will be in simulation. Second adjustment to the base model will be that simulation time will be prolongated to 8 hours. After running all 3 models, outputs will be compared and the optimal one will be selected.

'''Goal of simulation''' : In the previous rounds of COVID-19 mass testing in Slovakia certain sampling points had experienced massive overload and were not prepared for the amount of citizens incoming to be tested. Therefore, this simulation would aim to simulate the scenario with data from previous testing rounds and might be helpful if the governments decides to repeat mass testing again.

'''Method''' : Discrete simulation - SIMPROCESS

: The topic looks generaly good, my only concern is that is could be too simple. What steps of the model do you plan? Where do you obtain the real data? [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 02:54, 17 December 2020 (CET)

: I plan to obtain data from this site https://www.svidnik.sk/oznamy/druhe-kolo-plosneho-testovania-vysledky.html - on this website number of patients to be tested and number of points/places that take samples can be found. I know that each point/place has to have: 1 healthcare worker, 2 administrative workers and 1 police officer. Data about hourly rate can be obtained from this site: https://www.platy.sk/platy. Maybe I would like to adjust my original proposal, there would not be 1 point/place taking samples but 9 and I would create another simulation for more or less points/places. Generally I like the idea of splitting patients into two groups and I might include that in my simulation as well. One would consist of people older than 60 and the other one would consist of the rest of population. I will split the population according to demographic structure of Slovakia https://sk.wikipedia.org/wiki/Demografia_Slovenska#Vekov%C3%A1_%C5%A1trukt%C3%BAra. Steps I can think of right now: Patients entering, splitting the patients, administrative work, waiting, taking samples, waiting, receiving results, again splitting patients based on the results (negative ones can go home with certificate and positive ones would require additional steps like receiving information what to do next etc.) and the the simulation would end. [[User:Milan P|Milan P]] ([[User talk:MilanP|talk]]) 00:05, 18 December 2020 (CET)

==Operation of private dental office==

'''Author''' : [[User:Dufa00|Dufa00]] 10:50, 19 December 2020 (CET)

'''Simulation''' : I would simulate data and conditions of a real private dental office situated in central Bohemia. The Simulation will consist of the aspects influencing the company operations from within and from the outside. Nowadays even the COVID-19 is influencing the revenues and it would be interesting to see how it affects the company.

'''Goal of simulation''' : To help the specific dental office to react on possible dangers and see the hidden opportunities that might be available once the simulation is done. Whatsmore the results should be appliable to any other average private dental office.

'''Method''' : VensimPLE

about nanorobots vs. cancer: An interesting idea. Unfortunately, because this is completely unrealistic, you cannot work with any reasonable data and it means that you are not able to prove the meaningfulness of the results. Please suggest something else. [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 03:04, 17 December 2020 (CET)

update: I see, I was thinking that this might happen, is the new proposal better? [[User:Dufa00|Dufa00]] 11:03, 19. December 2020 (CET)

==Widening the spread between rich and poor==

'''Author''' : [[User:Sára|Sára]] 21:00, 14 December 2020 (CET)

'''Simulation''' : After 2007-9 world economic crisis a new monetary policy, rather unconventional, was established to escape recessions/depressions. It is called quantitative easing. Although this tool succeeded in reverting the depression and proved helpful during coming years, it is highly discussed what side effects this tool has. A lot of researches suggest that it widens the gap between rich and poor people and make prices of bonds and stocks highly overheated.

'''Goal of simulation''' : Based on macroeconomics theory and semantic experiences from quantitative easing and its influence on other macroeconomic agents like interest rate, inflation, monetary supply etc., i would like to simulate behavior of banks and people during quantitative easing and i would like to work with different values of macroeconomic agents and bank and people behavior in order to try to find out whether widening the spread between rich and poor is an unevitable effect, whether it is sustainable in long term and whether they are possibilities how to erase this side effect.

'''Method''' : NetLogo

: I like the topic (although quantitative easing is just an eufemism for money printing, hence the implications are quite predictable). Before I finally approve, please elaborate it deeper. How exactly you will simulate, what will be the agents, what will they do, etc. [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 02:47, 17 December 2020 (CET)

: Agents will be banks and people, until now quantitative easing is been applied always in the situation when interest rates were low for example, it makes people more willing to borrow but banks less willing to lend so idea behind my research is to simulate the process of quantitative easing under different circumstances than it is normally. According to different circumstances i will change people's and banks's behaviors according to macroeconomics theory and empirical knowledge. Is that deep enough? [[User:Sára|Sára]] ([[User talk:Sára|talk]]) 21:01, 18 December 2020 (CET)

==Rhino population in Africa==

'''Author''' : [[User:Michal F.|Michal F.]] ([[User talk:Michal F.|talk]]) 17:23, 15 December 2020 (CET)

'''Simulation''' : Rhinos once roamed many places in Europe, Asia, and Africa. At the beginning of the 20th century, about 500 000 rhinos roamed Africa and Asia. By 1970, rhino numbers dropped to 70,000, and today, around 27,000 rhinos remain in the wild. Africa's rhino population could face extinction within 10 years, animal welfare experts have warned. South Africa has the largest population of the species in the world however, the species still remains under threat from poaching for its horn and from habitat loss and degradation.
Data: http://www.rhinoresourcecenter.com/pdf_files/119/1192816187.pdf, http://www.scielo.org.za/pdf/koedoe/v59n1/15.pdf, https://rhinos.org/about-rhinos/rhino-species/black-rhino/

'''Goal of simulation''' : Based on the available data, I would like to simulate future development of the rhino population (probably the black ones in Africa, cause its most documented). The population is threatened by poaching and the loss of the natural environment. The shrinking population increases people's efforts to protect it from poachers but increases the demand for rhino horns.

'''Method''' : VensimPLE / Insight Maker

:: Topic is interesting. Can you specify the simulation in more detail - what would be the input parameters, variables, what all factors, that have an influence on rhino population, will be incorporated? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 14:55, 16 December 2020 (CET)

==Garbage collection==

'''Author''' : [[User:Dobj02|Dobj02]] ([[User talk:Dobj02|talk]]) 23:07, 16 December 2020 (CET)

'''Simulation''' : My aim is to simulate garbage collection in a city from the city counciler's point of view. I will focus on 3 main standpoints, specifically Waste production, Waste collection and Waste processing. The amount of produced waste is dependent on the population of the city and the rate of waste production of 1 person per day. Waste collection will be dependent on the amount of garbage trucks and their capacity. The number of employees (drivers and garbage collectors) will also play a role in how many trucks per day can be deployed. The final standpoint, Waste processing, consists of waste incineration and recycling. Incineration and recycling facilities can process different amount of waste per day. The scope of simulation can be either in weeks or months.

'''Goal of simulation''' : Finding balance between the amount of produced waste and its disposal by regulating the number of employees, trucks, their capacity, and the number of facilities which can either incinerate or recycle waste depending on the type of waste. The population of the city and the waste production of 1 person will be also adjustable.

'''Method''' : VensimPLE

::Sounds complex (maybe too complex) - but on what real data will you base the above described simulation on, so that the results would make sense? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 08:14, 18 December 2020 (CET)

Upon further reevaluation I propose to make the model simpler by crossing out the Waste collection standpoint, so there will be Waste production and Waste processing left. On these standpoints I found a valuable source of data: https://www.mzp.cz/cz/odpady_podrubrika . Also, thanks to the available data from 2009 to 2019 I could model the probable evolvement of waste production and waste processing either in Prague or the Czech republic. [[User:Dobj02|Dobj02]] ([[User talk:Dobj02|talk]]) 23:58, 18 December 2020 (CET)

::'''Approved''' and do not forget to include in the report for the simulation how you have derived the equations in the simulation from the data.[[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 13:48, 19 December 2020 (CET)

==Financial budget of football club==

'''Author''' : [[User:netp02|netp02]] ([[User talk:netp02|talk]]) 22:30, 17 December 2020 (CET)

'''Simulation''' :

The purpose of this simulation is to simulate important financial aspects of the football club. How much sponsors, players, transfers of players, money for tickets, number of sold club´s souvenir influence the budget of the clubs.

'''Goal of simulation''' :

Finding a balance between incomes and expenses, so the football club could work without any money donation from owner of the club.

'''Method''' : VensimPLE

:: On what real data will you base the above described simulation on, so that the results of your simulation would make sense? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 08:16, 18 December 2020 (CET)

:: I would take data from football club Slavia Prague, which announce almost all data for publicity. What it be possible to do it like that?
[[User:netp02|netp02]] ([[User talk:netp02|talk]]) 12:01, 18 December 2020 (CET)
::From the public data you cannot get know-how how a football club works on inside and therefore you cannot build complete system model with its feedback loops. If you would map only the financial flows, the system dynamics is no good for that and the result would be some kind of calcualtion, but not a simulation. I would suggest to try something else.[[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 19:27, 18 December 2020 (CET)

==IT Team simulation==

'''Simulation:'''

I would like to create a simulation, which is based on a Process Diagram and which would describe the process of solving business requirements within the IT team in which I now work. The simulation would show the entire course of the process from the origin of the request to the passage of all phases To Develop - Code review - Testing - Acceptance - UAT - Done.

'''Goal:'''

By simulation, I would deal with limited resources and limited specialization in the team. The goal would be to find out how many requests and in what rhythm our team would be able to deliver. As for the data basement - It would be based on the situation for the last two months. We solve projects in Jira and so I would be able to calculate how long the request lasted and when it returned to the previous stages + some average morbidity of team members, etc.

'''Method:''' SimProcess simulation

==COVID 19 symptoms==

'''Author''' : [[User:Stek15|Stek15]] ([[User talk:Stek15|talk]]) 11:31, 18 December 2020 (CET)

'''Simulation''' :

The model will represent COVID 19. The nodes in the model will represent the common symptoms of COVID 19. According to the World Health Organisation (WHO, 2020) there are 8 common symptoms: fever, dry cough, fatigue, shortness of breath, loss of appetite, confusion, persistent pain or pressure in the chest, high temperature (above 38 °C). The symptoms of said disease are thought to have direct causal relations with one another. If a person develops a symptom of COVID 19 (e.g. shortness of breath), this increases the likelihood of them developing other symptoms (e.g. loss of appetite, fever). Similarly, if one symptom disappears, the others might as well. The greatest danger is present for people vulnerable to the disease. The model will predict whether a person is vulnerable (due to high age) or resistant to the disease and take this in consideration.

'''Goal of simulation''' :

Each tick the probability of a symptom being developed will be calculated. The probability will depend on certain parameters + the total activation of the neighbouring symptoms at the previous tick. These parameters will be the supposed connection between the nodes (slider), influences unrelated to the disease (slider; said age or other respiratory diseases) and the threshold of each symptom.

'''Method''' : NetLogo

==Investment decision maker==

'''Author''' : [[User:mico00|mico00]] 18:13, 18 December 2020 (CET)

'''Simulation''' : the user has a limited amount of income, and can put in is certain funds. using monte-Carlo simulation, I'd like the user to be able to spread his funds to certain portfolios. these are prone to different oscillations and behavior throughout time. this becomes essentially a game, where the user has the power to work with his money, with the goal to maximize his profits after 10 year period. each transaction is punished by a certain amount of money for time costs.

'''Goal of simulation''' : Main goal is to learn how to handle money in an environment of uncertainty

'''Method''' : google sheets (essentially excel)

:: This is too general. There were some simulations like that in the past, just look for them in previous years. For this kind of task you have to specify what precisely you will simulate, where you will get the data for it (you will derive the probability distributions from), and what new features does your simulation brings compared to the assignments done in the past at this course. The good real data are a must for the MonteCarlo simulation. [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 19:36, 18 December 2020 (CET)

==Lawn Mower Roboter==

'''Author''' : [[User:Justin adenau|Justin adenau]] ([[User talk:Justin adenau|talk]]) 19:42, 18 December 2020 (CET)

'''Simulation''' : The Simulation will show the movement and efficiency of a lawn mower robot in different environments (gardens) with different obstacles. It will take attributes like frequency of lawing, wished height of grass, duration of lawing and the power consumption into account. Different algorithms for the movement and the treatment of obstacles will be tried. The limit for the lawing could be a wished height with a defined deviation which is not allowed to be exceeded. The data for the power consumption and duration of lawing can be extracted from variuos providers.

'''Goal of simulation''' : Optimize the lawing frequency and selected lawing height, so that the power consumption is the lowest and the deviation of the wished height of the grass is not exceeded.

'''Method''' : NETLogo

==Retirement Planning==

'''Author''' : [[User:Louis|Louis]] ([[User talk:Louis|talk]]) 19:59, 18 December 2020 (CET)

'''Simulation''' : Investing in shares can contribute a great deal to old-age provision. Therefore, I would like to simulate the portfolio decision of a young family. They already have a portfolio of shares and plan to continue investing a fixed amount each year. The decision is to continue to invest in a fixed stock index (SP500) or to invest in a portfolio of 4 CTX stocks from now on.

Data Source: Yahoo Finance

'''Goal of simulation''' : The aim of the simulation is to compare the two portfolios and calculate their probable value in 30 years and what interest income the family can expect in 30 years.

'''Method''' : Excel / Monte Carlo

==Covid 19 - Contract Tracing ==

'''Author''' : [[User:Carolin|Carolin]] ([[User talk:Carolin|talk]]) 21:19, 18 December 2020 (CET)

'''Simulation''' : The Covid 19 global pandemic has an impact on all our lives. Especially the lockdowns in all countries - including the Czech Republic and Germany. The main goal of these lockdowns is to reduce the number of contacts so that contacts of infected people can be traced and chains of infection can be broken. In my simulation, I would like to show the impact of higher distances between people and the prohibition of large public events on the number of infected people.
Contacts with infected people are represented by links, infections are shown by recoloring of the agent. The simulation will show the effects when wearing masks and when not.By this the simulation shows the effect in reducing infections by keeping distance, banning mass events and wearing masks.

'''Data Source''': Data on infection incidence sufficiently available - use only scientific sources

'''Goal of simulation''' : Showing the importance of keeping distance and holding onto rules in a global pandemic, to show the impact everbody has in these times.

'''Method''' : Netlogo

==Evolution of retirement pay in the Czech Republic ==

'''Author''' : [[User:Syca00|Syca00]] ([[User talk:Syca00|talk]]) 22:13, 18 December 2020 (CET)

'''Simulation''' : Nowadays a lot of people say that the Czech Republic will have problems with the retirement pay in the future. So, I decided to create a simulation, which will show a prediction of average retirement pay in the Czech Republic for next 50 years. The average retirement pay depends on more factors and I decided to predict it depending on GDP, state debt, population, mortality and natality.

'''Data Source''': I will use data from mfcr.cz and czso.cz

'''Goal of simulation''' : The aim of the simulation is to predict the evolution of average retirement pay in the Czech Republic and to find out how much money people will get in the future.

'''Method''' : VensimPLE

:: Topic is interesting, but the suggested simulation is too simple for such complex problem. Can you extend the simulation specification so that it matches the reality? (simulation of age groups, gross average wage, etc.) [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 13:56, 19 December 2020 (CET)

== Castle Siege ==

'''Author''' : [[User:Doum01|Doum01]] ([[User talk:Doum01|talk]]) 11:34, 19 December 2020 (CET)

'''Simulation''' : The simulation includes field area and the castle area, attacker agents will have to cross the field area which has an adjustable number of barricades and reach the gate in the castle area then sufficiently damage it to break it. Defender agents will shoot arrows from the castle walls to hinder attackers' progress and protect the gate and subsequently the castle. Attackers and defenders will have multiple types.

'''Data Source''': Number of attackers and defenders and value of their attributes will be adjustable by a common user.

'''Goal of simulation''' : Allowing user to generate custom scenarios and saving their results.

'''Method''' : Netlogo

== Hunting Sharks Simulation ==

'''Author''' : [[User:Frym06|Frym06]] ([[User talk:Frym06|talk]]) 11:56, 19 December 2020 (CET)

'''Simulation''' : I would like to create a simulation of life in the ocean, specifically shark hunts. In the simulation, there will be two types of agents, ''fish'' forming a shoal and ''sharks'' in an adjustable number. The first step will be to implement a swarm / shoal movement algorithm for ''fish'' agents. The ''fish'' will try to avoid the ''sharks'', although they will be slower, but much more mobile in changes of direction. They will also randomly spawn and die. ''Sharks'' will have two modes controlled by hunger. If the ''shark'' is full, it will just roam the ocean. If the ''shark'' is hungry, it switches to hunting mode. This is where the fun begins. The ''shark'' speeds up and starts hunting. When moving in one direction, its speed may increase even more. A ''shark'' in hunting mode will also have a greater vision range than ''fish''.
If there are more ''sharks'', it would be possible to implement reproduction or more types of food for ''shark'' (some can be more attractive for them).

'''Data Source''': Data traceable on the Internet, such as the swimming speed of sharks and common fish.

'''Goal of simulation''' : We do know that sharks are solitary animals, for the most part of live. They typically live and hunt by themselves, joining up with other sharks only in certain circumstances, such as mating. I would like to answer the question of whether it would be beneficial for sharks to form "packs".

'''Method''' : NetLogo

== Risk Simulation in Banking ==

'''Author''': [[User:Simon|Simon]] ([[User talk:Simon|talk]]) 13:40, 19 December 2020 (CET)

'''Simulation''': Since the Financial Crisis 2007/08 the systematic relevance of banks came into public focus. Excessive risk taking together with an interdependent banking sector led to a dangerous snowball effect which in most countries could only be fixed by massive bail-outs programs.
The exchange of liquidity in between commercial banks on the interbank market, while being beneficial in normal times, offers a treat to the systems stability during black swan events. I therefore plan to simulate the banking market in an arbitrary country and test its resilience to said events with different grades of safety mechanisms (like the Basel III rules for Capital requirements, leverage ratio and Liquidity requirements) in place.

'''Goal of Simulation''': The goal of the Simulation is to access the effectiveness of different measures that were introduced to bolster the financial systems stability. At the same time, I will try to fit the simulation parameters to those of the actual german banking market and try to derive the probabilities of a systematic collapse.

'''Data source''': Deutsche Bundesbank, ECB

'''Method''': Since the non-spatial nature of this topic, I think a MC-Simulation is the best method here.

:: Interesting topic. Can you specify the simulation in more detail - what would be the input parameters, variables, what all factors will be incorporated? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 13:52, 19 December 2020 (CET)

:: The input-parameters would be balance sheet information from the banks like leverage-ratio, liquidity or total assets (possibly with a projection over future years). Variables would be the default probabilities of other banks/private customers. Also I think about including certain "black swan" events like the bursting of housing bubbles or corona. [[User:Simon|Simon]] ([[User talk:Simon|talk]]) 14:17, 19 December 2020 (CET)

Assignments WS 2020/2021

2020-12-19T13:16:57Z

Simon:

Assignments WS 2020/2021

2020-12-19T12:41:14Z

Simon:

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Please, put here your assignments. Do not forget to sign them. You can use <nowiki>~~~~</nowiki> (four tildas) for an automatic signature. Use Show preview in order to check the result before your final sumbition.
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Please, strive to formulate your assignment carefully. We expect an adequate effort to formulate the assignment as it is your semestral paper. Do not forget that your main goal is a research paper. It means your simulation model must generate the results that are specific, measurable and verifiable. Think twice how you will develop your model, which entities you will use, draw a model diagram, consider what you will measure. No sooner than when you have a good idea about the model, submit your assignment. And of course, read [[How to deal with the simulation assignment|How to deal with the simulation assignment]].
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Topics on gambling, cards, etc. are not welcome.
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In order to avoid possible confusion, please, check if you have added '''approved''' in bold somewhere in our comment under your submission. If there is no '''approved''', it means the assignment was not approved yet.
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== Spread of 19-COVID ==
'''Author''' : [[User:Toscool|Toscool]] ([[User talk:Toscool|talk]]) 11:32, 11 December 2020 (CET)

'''Simulation''' : I will build a dynamic model of an epidemic his the dynamic issues. I will focus on the spread of Covid-19 in a population and Specially I will try to modelize the effect of a lockdown on the number of infections and deaths.
I will start with a susceptible population, with one infected people that infect 10 people with a certain probability. When you are infected you go the doctors and with a certain probability you go in the recovery population or in the hospital. Then you have a percentage of chance to die in this hospital or to recover. The lockdown will triggered when the ratio of people who where to the doctor and total population exceed a certain percentage. We lockdown and by reducing the number of people you infect in the beginning.

'''Goal of simulation''' : I aim to model the impact of a lockdown on the spread of COVID on a population. It will also show the difference between countries, for example if we lockdown too late. What will be the impact of these decisions.

'''Method''' : I will use VensimPLE for this simulation, as it is a dynamic system, and In my home university I know that I will need to use VensimPLE for a future project and course so it will help me a lot.

::The topic souds good - the question is, on what data sources will you base your simulation (equations) on? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 22:13, 12 December 2020 (CET)
:::I will use the case of Switzerland and use data from this website (https://corona-data.ch). I will try to reproduce the number of cases and the speed of the spread.[[User:Toscool|Toscool]] ([[User talk:Toscool|talk]]) 13:39, 13 December 2020 (CET)
::: OK. '''Approved''' but do not forget to include in the report for the simulation how you have derived the equations in the simulation from the data. [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 22:49, 14 December 2020 (CET)

== NFL Free Agency ==
'''Author''' : [[User:TimWalenczak|TimWalenczak]] ([[User talk:TimWalenczak|talk]]) 14:14, 18 December 2020 (CET)

'''Simulation''' : Free agency is a period during the off-season in the National Football League in the US. During that period, all 32 teams in the league can sign active players that have no contract with any other team, so-called free agents. The process goes as follows: at the beginning of free agency a certain amount of players become free agents due to expiring contracts. All players belong to one out of 8 position groups and want to receive a certain salary. Their starting position on the simulation grid is randomly assigned and they will move over the grid. The overall number of free agents is defined manually while they are randomly distributed over all position groups, as well as their desired salary, which is within a certain manually defined range. Whereas all the teams are looking for players from certain position groups and have a certain amount of money they can spend on them. The teams have fixed positions on the grid and do not move during the simulation. The maximum number of players a team is looking for is defined manually, while the desired position group is defined randomly from the list of position groups and the money to spend is randomly distributed over a certain manually defined salary range. When the simulation starts, the initial demand and supply ratio of a specific position is calculated and affects a player’s value. This means a player’s desired salary rises or decreases due to that demand and supply ratio. During the simulation players move over the grid. Players and teams get in touch when they are located next to each other. When a team’s position group needs matches the player’s position group and a player’s salary fits the money a team offers, the team signs this player and he disappears from the free agency market (turtle dies). If the offer doesn’t fit the need, a player walks on to the next team (turtle takes a random angle turn and walks until it approaches another team). Each team can negotiate only with one player at a time, and vice versa. With every round/tick/signing the demand and supply ratio is recalculated and the desired salary of all players in each position group changes and so does the amount of money teams are able to spend on further players (assuming they just signed a player). Free agency ends after a distinct number of ticks or even earlier if there are no more players left or teams do not have any money left to spend.

'''Goal of simulation''' : is to find out how a player’s value changes during the period of free agency. Especially interesting is, whether players that sign a new contract early in the period received higher payments or the ones signing late in the period. Maybe a certain strategy can be deducted for players depending on their initial demand and supply ratio in order to reach a highly paid contract.

'''Method''' : Since I don’t know VensimPLE yet, I think I will use NetLogo, because I see some similarities between my case and the “Market Structure” case we modelled recently.

: It is a bit unusual, but I can see something in common rather with Market Structure than with Building Escape. Please, just elaborate it into a greater detail and specify, how exactly should your simulation work. I am not sure you have a coherent idea about the solution. But if you work this out, I don't see a problem. [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 21:45, 11 December 2020 (CET)

: Yeah you are right I meant the Market Structure, sorry for the confusion! Okay, I updated the description above trying to go more into details. [[User:TimWalenczak|TimWalenczak]] ([[User talk:TimWalenczak|talk]]) 14:14, 18 December 2020 (CET)

==COVID-19 mass testing==

'''Author''' : [[User:Milan P|Milan P]] ([[User talk:MilanP|talk]]) 20:15, 13 December 2020 (CET)

'''Simulation''' : I will create simulation for mass Covid-19 testing in Slovakian village or small city. In previous rounds of this real mass testing in Slovakia testing itself took place in one day and in one sampling point, this will be the same with this simulation. In this model roles (medical staff, administrative workers, and police officer), will have assigned costs to them in order to include financial aspect into the simulation. Duration of the simulation will be 4 hours. This will serve as base model which will be adjusted in two ways. Firstly, I will create another model in which I will duplicate sampling point so 2 sampling points will be in simulation. Second adjustment to the base model will be that simulation time will be prolongated to 8 hours. After running all 3 models, outputs will be compared and the optimal one will be selected.

'''Goal of simulation''' : In the previous rounds of COVID-19 mass testing in Slovakia certain sampling points had experienced massive overload and were not prepared for the amount of citizens incoming to be tested. Therefore, this simulation would aim to simulate the scenario with data from previous testing rounds and might be helpful if the governments decides to repeat mass testing again.

'''Method''' : Discrete simulation - SIMPROCESS

: The topic looks generaly good, my only concern is that is could be too simple. What steps of the model do you plan? Where do you obtain the real data? [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 02:54, 17 December 2020 (CET)

: I plan to obtain data from this site https://www.svidnik.sk/oznamy/druhe-kolo-plosneho-testovania-vysledky.html - on this website number of patients to be tested and number of points/places that take samples can be found. I know that each point/place has to have: 1 healthcare worker, 2 administrative workers and 1 police officer. Data about hourly rate can be obtained from this site: https://www.platy.sk/platy. Maybe I would like to adjust my original proposal, there would not be 1 point/place taking samples but 9 and I would create another simulation for more or less points/places. Generally I like the idea of splitting patients into two groups and I might include that in my simulation as well. One would consist of people older than 60 and the other one would consist of the rest of population. I will split the population according to demographic structure of Slovakia https://sk.wikipedia.org/wiki/Demografia_Slovenska#Vekov%C3%A1_%C5%A1trukt%C3%BAra. Steps I can think of right now: Patients entering, splitting the patients, administrative work, waiting, taking samples, waiting, receiving results, again splitting patients based on the results (negative ones can go home with certificate and positive ones would require additional steps like receiving information what to do next etc.) and the the simulation would end. [[User:Milan P|Milan P]] ([[User talk:MilanP|talk]]) 00:05, 18 December 2020 (CET)

==Operation of private dental office==

'''Author''' : [[User:Dufa00|Dufa00]] 10:50, 19 December 2020 (CET)

'''Simulation''' : I would simulate data and conditions of a real private dental office situated in central Bohemia. The Simulation will consist of the aspects influencing the company operations from within and from the outside. Nowadays even the COVID-19 is influencing the revenues and it would be interesting to see how it affects the company.

'''Goal of simulation''' : To help the specific dental office to react on possible dangers and see the hidden opportunities that might be available once the simulation is done. Whatsmore the results should be appliable to any other average private dental office.

'''Method''' : VensimPLE

about nanorobots vs. cancer: An interesting idea. Unfortunately, because this is completely unrealistic, you cannot work with any reasonable data and it means that you are not able to prove the meaningfulness of the results. Please suggest something else. [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 03:04, 17 December 2020 (CET)

update: I see, I was thinking that this might happen, is the new proposal better? [[User:Dufa00|Dufa00]] 11:03, 19. December 2020 (CET)

==Widening the spread between rich and poor==

'''Author''' : [[User:Sára|Sára]] 21:00, 14 December 2020 (CET)

'''Simulation''' : After 2007-9 world economic crisis a new monetary policy, rather unconventional, was established to escape recessions/depressions. It is called quantitative easing. Although this tool succeeded in reverting the depression and proved helpful during coming years, it is highly discussed what side effects this tool has. A lot of researches suggest that it widens the gap between rich and poor people and make prices of bonds and stocks highly overheated.

'''Goal of simulation''' : Based on macroeconomics theory and semantic experiences from quantitative easing and its influence on other macroeconomic agents like interest rate, inflation, monetary supply etc., i would like to simulate behavior of banks and people during quantitative easing and i would like to work with different values of macroeconomic agents and bank and people behavior in order to try to find out whether widening the spread between rich and poor is an unevitable effect, whether it is sustainable in long term and whether they are possibilities how to erase this side effect.

'''Method''' : NetLogo

: I like the topic (although quantitative easing is just an eufemism for money printing, hence the implications are quite predictable). Before I finally approve, please elaborate it deeper. How exactly you will simulate, what will be the agents, what will they do, etc. [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 02:47, 17 December 2020 (CET)

: Agents will be banks and people, until now quantitative easing is been applied always in the situation when interest rates were low for example, it makes people more willing to borrow but banks less willing to lend so idea behind my research is to simulate the process of quantitative easing under different circumstances than it is normally. According to different circumstances i will change people's and banks's behaviors according to macroeconomics theory and empirical knowledge. Is that deep enough? [[User:Sára|Sára]] ([[User talk:Sára|talk]]) 21:01, 18 December 2020 (CET)

==Rhino population in Africa==

'''Author''' : [[User:Michal F.|Michal F.]] ([[User talk:Michal F.|talk]]) 17:23, 15 December 2020 (CET)

'''Simulation''' : Rhinos once roamed many places in Europe, Asia, and Africa. At the beginning of the 20th century, about 500 000 rhinos roamed Africa and Asia. By 1970, rhino numbers dropped to 70,000, and today, around 27,000 rhinos remain in the wild. Africa's rhino population could face extinction within 10 years, animal welfare experts have warned. South Africa has the largest population of the species in the world however, the species still remains under threat from poaching for its horn and from habitat loss and degradation.
Data: http://www.rhinoresourcecenter.com/pdf_files/119/1192816187.pdf, http://www.scielo.org.za/pdf/koedoe/v59n1/15.pdf, https://rhinos.org/about-rhinos/rhino-species/black-rhino/

'''Goal of simulation''' : Based on the available data, I would like to simulate future development of the rhino population (probably the black ones in Africa, cause its most documented). The population is threatened by poaching and the loss of the natural environment. The shrinking population increases people's efforts to protect it from poachers but increases the demand for rhino horns.

'''Method''' : VensimPLE / Insight Maker

:: Topic is interesting. Can you specify the simulation in more detail - what would be the input parameters, variables, what all factors, that have an influence on rhino population, will be incorporated? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 14:55, 16 December 2020 (CET)

==Garbage collection==

'''Author''' : [[User:Dobj02|Dobj02]] ([[User talk:Dobj02|talk]]) 23:07, 16 December 2020 (CET)

'''Simulation''' : My aim is to simulate garbage collection in a city from the city counciler's point of view. I will focus on 3 main standpoints, specifically Waste production, Waste collection and Waste processing. The amount of produced waste is dependent on the population of the city and the rate of waste production of 1 person per day. Waste collection will be dependent on the amount of garbage trucks and their capacity. The number of employees (drivers and garbage collectors) will also play a role in how many trucks per day can be deployed. The final standpoint, Waste processing, consists of waste incineration and recycling. Incineration and recycling facilities can process different amount of waste per day. The scope of simulation can be either in weeks or months.

'''Goal of simulation''' : Finding balance between the amount of produced waste and its disposal by regulating the number of employees, trucks, their capacity, and the number of facilities which can either incinerate or recycle waste depending on the type of waste. The population of the city and the waste production of 1 person will be also adjustable.

'''Method''' : VensimPLE

::Sounds complex (maybe too complex) - but on what real data will you base the above described simulation on, so that the results would make sense? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 08:14, 18 December 2020 (CET)

Upon further reevaluation I propose to make the model simpler by crossing out the Waste collection standpoint, so there will be Waste production and Waste processing left. On these standpoints I found a valuable source of data: https://www.mzp.cz/cz/odpady_podrubrika . Also, thanks to the available data from 2009 to 2019 I could model the probable evolvement of waste production and waste processing either in Prague or the Czech republic. [[User:Dobj02|Dobj02]] ([[User talk:Dobj02|talk]]) 23:58, 18 December 2020 (CET)

==Financial budget of football club==

'''Author''' : [[User:netp02|netp02]] ([[User talk:netp02|talk]]) 22:30, 17 December 2020 (CET)

'''Simulation''' :

The purpose of this simulation is to simulate important financial aspects of the football club. How much sponsors, players, transfers of players, money for tickets, number of sold club´s souvenir influence the budget of the clubs.

'''Goal of simulation''' :

Finding a balance between incomes and expenses, so the football club could work without any money donation from owner of the club.

'''Method''' : VensimPLE

:: On what real data will you base the above described simulation on, so that the results of your simulation would make sense? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 08:16, 18 December 2020 (CET)

:: I would take data from football club Slavia Prague, which announce almost all data for publicity. What it be possible to do it like that?
[[User:netp02|netp02]] ([[User talk:netp02|talk]]) 12:01, 18 December 2020 (CET)
::From the public data you cannot get know-how how a football club works on inside and therefore you cannot build complete system model with its feedback loops. If you would map only the financial flows, the system dynamics is no good for that and the result would be some kind of calcualtion, but not a simulation. I would suggest to try something else.[[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 19:27, 18 December 2020 (CET)

==IT Team simulation==

'''Simulation:'''

I would like to create a simulation, which is based on a Process Diagram and which would describe the process of solving business requirements within the IT team in which I now work. The simulation would show the entire course of the process from the origin of the request to the passage of all phases To Develop - Code review - Testing - Acceptance - UAT - Done.

'''Goal:'''

By simulation, I would deal with limited resources and limited specialization in the team. The goal would be to find out how many requests and in what rhythm our team would be able to deliver. As for the data basement - It would be based on the situation for the last two months. We solve projects in Jira and so I would be able to calculate how long the request lasted and when it returned to the previous stages + some average morbidity of team members, etc.

'''Method:''' SimProcess simulation

==COVID 19 symptoms==

'''Author''' : [[User:Stek15|Stek15]] ([[User talk:Stek15|talk]]) 11:31, 18 December 2020 (CET)

'''Simulation''' :

The model will represent COVID 19. The nodes in the model will represent the common symptoms of COVID 19. According to the World Health Organisation (WHO, 2020) there are 8 common symptoms: fever, dry cough, fatigue, shortness of breath, loss of appetite, confusion, persistent pain or pressure in the chest, high temperature (above 38 °C). The symptoms of said disease are thought to have direct causal relations with one another. If a person develops a symptom of COVID 19 (e.g. shortness of breath), this increases the likelihood of them developing other symptoms (e.g. loss of appetite, fever). Similarly, if one symptom disappears, the others might as well. The greatest danger is present for people vulnerable to the disease. The model will predict whether a person is vulnerable (due to high age) or resistant to the disease and take this in consideration.

'''Goal of simulation''' :

Each tick the probability of a symptom being developed will be calculated. The probability will depend on certain parameters + the total activation of the neighbouring symptoms at the previous tick. These parameters will be the supposed connection between the nodes (slider), influences unrelated to the disease (slider; said age or other respiratory diseases) and the threshold of each symptom.

'''Method''' : NetLogo

==Investment decision maker==

'''Author''' : [[User:mico00|mico00]] 18:13, 18 December 2020 (CET)

'''Simulation''' : the user has a limited amount of income, and can put in is certain funds. using monte-Carlo simulation, I'd like the user to be able to spread his funds to certain portfolios. these are prone to different oscillations and behavior throughout time. this becomes essentially a game, where the user has the power to work with his money, with the goal to maximize his profits after 10 year period. each transaction is punished by a certain amount of money for time costs.

'''Goal of simulation''' : Main goal is to learn how to handle money in an environment of uncertainty

'''Method''' : google sheets (essentially excel)

:: This is too general. There were some simulations like that in the past, just look for them in previous years. For this kind of task you have to specify what precisely you will simulate, where you will get the data for it (you will derive the probability distributions from), and what new features does your simulation brings compared to the assignments done in the past at this course. The good real data are a must for the MonteCarlo simulation. [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 19:36, 18 December 2020 (CET)

==Lawn Mower Roboter==

'''Author''' : [[User:Justin adenau|Justin adenau]] ([[User talk:Justin adenau|talk]]) 19:42, 18 December 2020 (CET)

'''Simulation''' : The Simulation will show the movement and efficiency of a lawn mower robot in different environments (gardens) with different obstacles. It will take attributes like frequency of lawing, wished height of grass, duration of lawing and the power consumption into account. Different algorithms for the movement and the treatment of obstacles will be tried. The limit for the lawing could be a wished height with a defined deviation which is not allowed to be exceeded. The data for the power consumption and duration of lawing can be extracted from variuos providers.

'''Goal of simulation''' : Optimize the lawing frequency and selected lawing height, so that the power consumption is the lowest and the deviation of the wished height of the grass is not exceeded.

'''Method''' : NETLogo

==Retirement Planning==

'''Author''' : [[User:Louis|Louis]] ([[User talk:Louis|talk]]) 19:59, 18 December 2020 (CET)

'''Simulation''' : Investing in shares can contribute a great deal to old-age provision. Therefore, I would like to simulate the portfolio decision of a young family. They already have a portfolio of shares and plan to continue investing a fixed amount each year. The decision is to continue to invest in a fixed stock index (SP500) or to invest in a portfolio of 4 CTX stocks from now on.

Data Source: Yahoo Finance

'''Goal of simulation''' : The aim of the simulation is to compare the two portfolios and calculate their probable value in 30 years and what interest income the family can expect in 30 years.

'''Method''' : Excel / Monte Carlo

==Covid 19 - Contract Tracing ==

'''Author''' : [[User:Carolin|Carolin]] ([[User talk:Carolin|talk]]) 21:19, 18 December 2020 (CET)

'''Simulation''' : The Covid 19 global pandemic has an impact on all our lives. Especially the lockdowns in all countries - including the Czech Republic and Germany. The main goal of these lockdowns is to reduce the number of contacts so that contacts of infected people can be traced and chains of infection can be broken. In my simulation, I would like to show the impact of higher distances between people and the prohibition of large public events on the number of infected people.
Contacts with infected people are represented by links, infections are shown by recoloring of the agent. The simulation will show the effects when wearing masks and when not.By this the simulation shows the effect in reducing infections by keeping distance, banning mass events and wearing masks.

'''Data Source''': Data on infection incidence sufficiently available - use only scientific sources

'''Goal of simulation''' : Showing the importance of keeping distance and holding onto rules in a global pandemic, to show the impact everbody has in these times.

'''Method''' : Netlogo

==Evolution of retirement pay in the Czech Republic ==

'''Author''' : [[User:Syca00|Syca00]] ([[User talk:Syca00|talk]]) 22:13, 18 December 2020 (CET)

'''Simulation''' : Nowadays a lot of people say that the Czech Republic will have problems with the retirement pay in the future. So, I decided to create a simulation, which will show a prediction of average retirement pay in the Czech Republic for next 50 years. The average retirement pay depends on more factors and I decided to predict it depending on GDP, state debt, population, mortality and natality.

'''Data Source''': I will use data from mfcr.cz and czso.cz

'''Goal of simulation''' : The aim of the simulation is to predict the evolution of average retirement pay in the Czech Republic and to find out how much money people will get in the future.

'''Method''' : VensimPLE

== Castle Siege ==

'''Author''' : [[User:Doum01|Doum01]] ([[User talk:Doum01|talk]]) 11:34, 19 December 2020 (CET)

'''Simulation''' : The simulation includes field area and the castle area, attacker agents will have to cross the field area which has an adjustable number of barricades and reach the gate in the castle area then sufficiently damage it to break it. Defender agents will shoot arrows from the castle walls to hinder attackers' progress and protect the gate and subsequently the castle. Attackers and defenders will have multiple types.

'''Data Source''': Number of attackers and defenders and value of their attributes will be adjustable by a common user.

'''Goal of simulation''' : Allowing user to generate custom scenarios and saving their results.

'''Method''' : Netlogo

== Hunting Sharks Simulation ==

'''Author''' : [[User:Frym06|Frym06]] ([[User talk:Frym06|talk]]) 11:56, 19 December 2020 (CET)

'''Simulation''' : I would like to create a simulation of life in the ocean, specifically shark hunts. In the simulation, there will be two types of agents, ''fish'' forming a shoal and ''sharks'' in an adjustable number. The first step will be to implement a swarm / shoal movement algorithm for ''fish'' agents. The ''fish'' will try to avoid the ''sharks'', although they will be slower, but much more mobile in changes of direction. They will also randomly spawn and die. ''Sharks'' will have two modes controlled by hunger. If the ''shark'' is full, it will just roam the ocean. If the ''shark'' is hungry, it switches to hunting mode. This is where the fun begins. The ''shark'' speeds up and starts hunting. When moving in one direction, its speed may increase even more. A ''shark'' in hunting mode will also have a greater vision range than ''fish''.
If there are more ''sharks'', it would be possible to implement reproduction or more types of food for ''shark'' (some can be more attractive for them).

'''Data Source''': Data traceable on the Internet, such as the swimming speed of sharks and common fish.

'''Goal of simulation''' : We do know that sharks are solitary animals, for the most part of live. They typically live and hunt by themselves, joining up with other sharks only in certain circumstances, such as mating. I would like to answer the question of whether it would be beneficial for sharks to form "packs".

'''Method''' : NetLogo

== Risk Simulation in Banking ==

'''Author''': [[User:Simon|Simon]] ([[User talk:Simon|talk]]) 13:40, 19 December 2020 (CET)

'''Simulation''': Since the Financial Crisis 2007/08 the systematic relevance of banks came into public focus. Excessive risk taking together with an interdependent banking sector led to a dangerous snowball effect which in most countries could only be fixed by massive bail-outs programs.
The exchange of liquidity in between commercial banks on the interbank market, while being beneficial in normal times, offers a treat to the systems stability during black swan events. I therefore plan to simulate the banking market in an arbitrary country and test its resilience to said events with different grades of safety mechanisms (like the Basel III rules for Capital requirements, leverage ratio and Liquidity requirements) in place.

'''Goal of Simulation''': The goal of the Simulation is to access the effectiveness of different measures that were introduced to bolster the financial systems stability. At the same time, I will try to fit the simulation parameters to those of the actual german banking market and try to derive the probabilities of a systematic collapse.

'''Data source''': Deutsche Bundesbank, ECB

'''Method''': Since the non-spatial nature of this topic, I think a MC-Simulation is the best method here.