pavel v. shevchenko quantitative risk management csiro ... · • basel ii requires that banks hold...

Quantitative modelling of financial risks

Pavel V. ShevchenkoQuantitative Risk Management

CSIRO Mathematical and Information Sciences

Vienna University of Technology12 January 2010

CSIRO Mathematical & Information Sciences www.cmis.csiro.au

CSIRO Mathematical and Information Sciences

Commonwealth Industrial Research Organisation (CSIRO) AustraliaMathematical and Information Sciences (CMIS)Financial risk teamIndustry: banks, insurance/electricity companies, hedge fundsActivities/modes of engagement: strategic research, consulting, model

development/validation, software developmentBeneficiaries of our work in risk management:• Financial institutions and their shareholders (risk reduction)• Stability of banking/insurance systems• Science and CMISOur mission – To conduct research in financial risk quantification,

measurement and calculation; To develop innovative quantitativemethods and tools in financial engineering


Financial Risks – quantifying uncertainties

Risks are modelled by random variables mapping unforeseen future states of the world into values representing profits and losses.

Market Risk: modelling of losses incurred on a trading book due market movements (interest rates, exchange rates, etc)

Credit risk: modelling of losses from credit downgrades and defaults (e.g. loan defaults)

Operational Risk: modelling of losses due to failed internal processes, people or external events (e.g. human errors, IT failures, natural disasters, etc)

Quantifying the uncertainties: process uncertainty, parameter uncertainty, numerical error, model error


Links•Extreme Value models•Expert Elicitation•Combining expert&data•Bayesian methods•Dependence modelling•Numerical methods (PDE, MCMC, MC)•Time series analysis•State-space models•High performance computing•Optimisation

Other risk areas•Air transport•Ecology•Environment•Infrastructure •Security•Weather/Climate•Health

Financial Risk• Market Risk • Credit Risk • Operational Risk• Underwriting risk • Derivative pricing• Interest Rates• Trading strategies• Portfolio Management• Commodity/Energy• Carbon Trading• Liquidity risk

Financial risk and other risk areas


Regulatory Requirements for banking industry

•Regulatory standards in banking industry:Basel Committee for banking supervision 1974Basel I, 1988: Credit Risk, Basel I Amendment 1996: Market Risk (VaR) Basel II 2001- ongoing: Credit Risk, Operational Risk

•Insurance regulation: International Association of Insurance SupervisorsJoint Forum on Financial Conglomerates 1996Solvency II (similar to Basel II for banks)


2010 - Basel III?


Basel II• Basel II requires that banks hold adequate capital to protect

against Market risk, Credit risk and Operational Risk losses. Three-pillar framework:

Pillar 1: minimal capital requirements (risk measurement)Pillar 2: supervisory review of capital adequacyPillar 3: public disclosure

Advanced Measurement Approaches allow internal models for calculations of capital as a large quantile of loss distribution.Operational Risk is new risk category

• In Australia, the national regulator APRA is now applying the Basel II requirements.

• Solvency 2 for insurance industry


Regulatory Requirements – Risk MeasuresValue at Risk (VaR)

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Operational Risk: Loss Distribution Approach

• Severity Distribution type F(x):e.g. Lognormal, Gamma, Pareto, g-and-h, EVT, mixtures

• Frequency distributions P(N): e.g. Poisson, Negative Binomial, Binomial

• Annual loss

• Typical assumptions:

• Distribution of Z: Monte Carlo, Fast Fourier Transform, Panjerrecursion, direct inversion of characteristic Functions.

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Basel II, Operational Risk

•Basel II defined Operational Risk as: the risk of loss resulting from inadequate or failed internal processes, people and systemsor from external events. This definition includes legal risk but excludes strategic and reputational risk.

•Losses can be extreme, e.g.1995: Barings Bank (loss GBP1.3billion)1996: Sumitomo Corporation (loss US$2.6billion)2001: September 112001: Enron, USD 2.2b (largest US bankruptcy so far)2002: Allied Irish, £450m2004: National Australia bank (A$360m)2008: Société Générale (Euro 4.9billion)


Basel II Operational Risk

Three-pillar framework:• Pillar 1: minimal capital requirements (risk measurement)• Pillar 2: supervisory review of capital adequacy• Pillar 3: public disclosure

Operation Risk Capital Charge• The Basic Indicator Approach:

GI(j) is Gross Income in year j.• The Standardised Approach: (12-18% per business line)

• The Advanced Measurement Approaches (AMA): Internal model for 56 risk cells (7 event types x 8 business lines)

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Operational Risk Basel II Business Lines/Event Types

Basel II Business Lines (BL)• BL(1) - Corporate finance• BL(2) - Trading & Sales• BL(3) - Retail banking• BL(4) - Commercial banking• BL(5) - Payment & Settlement• BL(6) - Agency Services• BL(7) - Asset management• BL(8) - Retail brokerage

Basel II Event Type (ET)•ET(1) - Internal fraud:•ET(2) - External fraud: •ET(3) - Employment practices and

workplace safety: •ET(4) - Clients, products and

business practices•ET(5) - Damage to physical assets:•ET(6) - Business disruption and

system failures: •ET(7) - Execution, delivery and

process management:


Hierarchical and matrix structures

Business Line (BL) Risk Type (RT)

top levelBL1

BL8

BLi

RT1 RT7RTk

Basel II risk matrix

Zik

Bank hierarchical structure


Loss Data Collection Exercise 2007 Japan - Annualized data: Number of events(100%=947.7) / Total Loss Amount (100%=JPY 22,650mln)

100% (no.events)100% (loss)

38.6%54.6%

10.9%3.9%

1.9%4.5%

8.8%24.8%

1.5%1.0%

36.5%8.3%

1.8%2.9%

Total

0.4%0.2%

0.02%0.00%

0.09%0.00%

0.13%0.00%

0.00%0.00%

0.02%0.00%

0.11%0.00%

0.09%0.18%

Other

3.5%2.0%

1.06%0.13%

0.18%0.04%

0.00%0.00%

1.40%0.53%

0.01%0.00%

0.00%0.00%

0.84%1.32%

BL(8)

2.1%1.5%

1.50%1.02%

0.05%0.00%

0.00%0.00%

0.48%0.49%

0.1%0.04%

0.00%0.00%

0.00%0.00%

BL(7)

5.3%3.8%

3.14%3.00%

1.19%0.22%

0.01%0.00%

0.92%0.62%

0.01%0.00%

0.00%0.00%

0.00%0.00%

BL(6)

0.6%0.1%

0.23%0.00%

0.38%0.04%

0.00%0.00%

0.00%0.00%

0.00%0.00%

0.00%0.00%

0.00%0.00%

BL(5)

25.7%45.4%

15.05%16.87%

5.87%3.22%

0.69%4.19%

2.02%18.32%

1.16%0.71%

0.64%1.99%

0.29%0.13%

BL(4)

57.2%21.5%

13.21%8.43%

2.83%0.26%

1.11%0.26%

3.62%4.77%

0.14%0.18%

35.73%6.36%

0.54%1.24%

BL(3)

4.7%25.2%

4.12%25.03%

0.26%0.00%

0.00%0.00%

0.22%0.09%

0.04%0.04%

0.00%0.00%

0.01%0.00%

BL(2)

0.5%0.3%

0.28%0.18%

0.07%0.04%

0.00%0.00%

0.11%0.09%

0.01%0.00%

0.01%0.00%

0.00%0.00%

BL(1)

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Loss Data Collection Exercise 2004 USA - Annualized data: Number of events(100%=18371) / Total Loss Amount (100%=USD 8,643mln)

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3.2%0.6%

0.8%0.1%

35.3%9.6%

0.7%0.8%

0.7%1.4%

9.2%79.8%

7.6%1.7%

39.0%5.1%

3.40%0.9%

Total

8.0%70.8%

0.08%0.01%

0.07%0.05%

3.45%0.98%

0.02%0.44%

0.12%1.28%

0.40%67.34%

1.75%0.34%

1.66%0.3%

0.42%0.1%

Other

7.3%1.6%

0.20%0.07%

2.20%0.25%

0.01%0.00%

3.30%0.94%

1.38%0.33%

0.10%0.02%

0.06%0.03%

BL(8)

2.4%2.5%

0.09%0.01%

1.82%0.38%

0.04%0.01%

0.00%0.00%

0.13%2.10%

0.10%0.02%

0.26%0.02%

0.00%0.00%

BL(7)

5.1%1.1%

4.52%0.99%

0.14%0.02%

0.01%0.01%

0.31%0.06%

0.04%0.02%

0.03%0.01%

0.01%0.02%

BL(6)

4.5%0.6%

0.23%0.05%

0.01%0.00%

2.99%0.28%

0.05%0.02%

0.01%0.00%

0.04%0.01%

0.18%0.02%

0.44%0.13%

0.52%0.08%

BL(5)

5.1%1.8%

0.44%0.04%

0.02%0.00%

1.38%0.28%

0.03%0.00%

0.01%0.00%

0.36%0.78%

0.17%0.03%

2.64%0.70%

0.05%0.01%

BL(4)

60.1%12.3%

2.10%0.26%

0.69%0.06%

12.28%3.66%

0.21%0.21%

0.56%0.1%

4.41%4.01%

3.76%0.87%

33.85%2.75%

2.29%0.42%

BL(3)

7.3%8.6%

0.05%0.15%

6.55%2.76%

0.24%0.06%

0.03%0.00%

0.19%4.29%

0.17%0.05%

0.01%1.17%

0.02%0.10%

BL(2)

0.3%0.5%

0.01%0.00%

0.03%0.01%

0.12%0.05%

0.00%0.00%

0.08%0.30%

0.06%0.03%

0.01%0.00%

0.01%0.14%

BL(1)

TotalFraudOtherET(7)ET(6)ET(5)ET(4)ET(3)ET(2)ET(1)


Internal

Loss Data

External

Loss Data

Scenario analysis

Risk Frequency and Severity distributions

Annual loss distribution (per risk and over all risks)

Annual Capital Charge (Capital Allocation, sensitivity, what if scenarios)

Business environment and internal control factors

Insurance Dependence between risks

Operational Risk - Loss Distribution Approach

Monte Carlo simulations


Operational Risk: Combining internal data, industry data and expert opinions

• BIS (2006), p.152: “Any operational risk measurement system must have certain key features to meet the supervisory soundnessstandard set out in this section. These elements must include the use of internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal controlsystems.”

• An interview with four industry’s top risk executives: Davis, E. (1 September 2006). Theory vs Reality, OpRisk and Compliance: “[A] big challenge for us is how to mix the internal data with external data; this is something that is still a big problem because I don’t think anybody has a solution for that at the moment.” Or: “What can we do when we don’t have enough data [. . .] How do I use a small amount of data when I can have external data with scenario generation? [. . .] I think it is one of the big challenges for operational risk managers at the moment”.


Ad-hoc procedures for combining internal data, industry data and expert opinions (SA)

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Relative bias in the 0.999 quantile estimator induced by the parameter uncertainty vs number of observation years. (Lognormal) - losses were simulated from Poisson(10) and LN(1,2). (Pareto) – losses were simulated from Poisson(10) and Pareto(2) with L=1.


Research topics for collaboration

• Combining different data sources: internal & external data with expert opinions (credibility theory, Bayesian techniques)

• Dependence between risks: copula methods, structural models• Expert elicitation (Bayesian networks) • Extreme Value Models (Modelling distribution tail)• Efficient Markov Chain Monte Carlo, ABC MCMC, Monte Carlo, finite

element/finite difference methods • State-space models (Kalman/particle filters/SMC)

• Pattern recognition – trading strategies • Stochastic/local volatility models• Modelling operational/market/credit risks/insurance risks• Pricing exotic options• Modelling commodities, interest rates, • Portfolio asset allocation

Thank youCSIRO Mathematical & Information SciencesPavel ShevchenkoEmail: [email protected]/Pavel.Shevchenkowww.csiro.au/people/Pavel.Shevchenko.html

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

George Box and Norman Draper (1987)


Recent journal publications

• X. Luo and P.V. Shevchenko (2009). The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk Management. Quantitative Finance.

• G. W. Peters, P. V. Shevchenko and M. V. Wüthrich (2009). Model uncertainty in claims reserving within Tweedie's compound Poisson models. ASTIN Bulletin 39(1), 1-33.

• P. V. Shevchenko (2009). Implementing loss distribution approach for operational risk. Applied Stochastic Models in Business and Industry.

• Peters, G., P. Shevchenko and M.Wuthrich (2009). Dynamic operational risk: modellingdependence and combining different data sources of information. The Journal of Operational Risk 4(2), 69-104.

• Shevchenko, P. (2008). Estimation of Operational Risk Capital Charge under Parameter Uncertainty. The Journal of Operational Risk 3(1), 51-63.

• Luo, X., P. V. Shevchenko and J. Donnelly (2007). Addressing Impact of Truncation and Parameter Uncertainty on Operational Risk Estimates. The Journal of Operational Risk 2(4), 3-26.

• D. D. Lambrigger, P.V. Shevchenko and M. V. Wüthrich (2007). The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions. The Journal of Operational Risk 2(3), 3-27.

• Bühlmann,H., P. Shevchenko and M. Wüthrich. A “Toy” Model for Operational Risk Quantification using Credibility Theory. The Journal of Operational Risk 2(1), 3-19, 2007.

• Shevchenko, P. and M. Wüthrich (2006). Structural Modelling of Operational Risk using Bayesian Inference: combining loss data with expert opinions. The Journal of Operational Risk1(3), 3-26.

pavel v. shevchenko quantitative risk management csiro ... · • basel ii requires that banks hold...

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