درک ریسک بازار، اعتبار و عملیاتی: رویکرد ارزش در معرض خطر ۲۰۰۹
Understanding Market, Credit, and Operational Risk: The Value at Risk Approach 2009

1. LIST OF FIGURES

2. LIST OF TABLES

3. PREFACE

4. LIST OF ABBREVIATIONS

1 INTRODUCTION TO VALUE AT RISK (VaR)

1.1 ECONOMICS UNDERLYING VaR MEASUREMENT

1.1.1 What is VaR?

1.1.2 Calculating VaR

1.1.3 The assumptions behind VaR calculations

1.1.4 Inputs into VaR calculations

1.2 DIVERSIFICATION AND VaR

1.2.1 Factors affecting portfolio diversification

1.2.2 Decomposing volatility into systematic and idiosyncratic risk

1.2.3 Diversification: Words of caution – the case of long-term capital management (LTCM)

2 QUANTIFYING VOLATILITY IN VaR MODELS

2.1 THE STOCHASTIC BEHAVIOR OF RETURNS

2.1.1 Revisiting the assumptions

2.1.2 The distribution of interest rate changes

2.1.3 Fat tails

2.1.4 Explaining fat tails

2.1.5 Effects of volatility changes

2.1.6 Can (conditional) normality be salvaged?

2.1.7 Normality cannot be salvaged

2.2 VaR ESTIMATION APPROACHES

2.2.1 Cyclical volatility

2.2.2 Historical standard deviation

2.2.3 Implementation considerations

2.2.4 Exponential smoothing – RiskMetrics™ volatility

2.2.4.1 The optimal smoother lambda

2.2.4.2 Adaptive volatility estimation

2.2.4.3 The empirical performance of RiskMetrics™

2.2.4.4 GARCH

2.2.5 Nonparametric volatility forecasting

2.2.5.1 Historical simulation

2.2.5.2 Multivariate density estimation

2.2.6 A comparison of methods

2.2.7 The hybrid approach

2.3 RETURN AGGREGATION AND VaR

2.4 IMPLIED VOLATILITY AS A PREDICTOR OF FUTURE VOLATILITY

2.5 LONG HORIZON VOLATILITY AND VaR

2.6 MEAN REVERSION AND LONG HORIZON VOLATILITY

2.7 CORRELATION MEASUREMENT

2.8 SUMMARY

44. APPENDIX 2.1 BACKTESTING METHODOLOGY AND RESULTS

3 PUTTING VaR TO WORK

3.1 THE VaR OF DERIVATIVES – PRELIMINARIES

3.1.1 Linear derivatives

3.1.2 Nonlinear derivatives

3.1.3 Approximating the VaR of derivatives

3.1.4 Fixed income securities with embedded optionality

3.1.5 “Delta normal” vs. full-revaluation

3.2 STRUCTURED MONTE CARLO, STRESS TESTING, AND SCENARIO ANALYSIS

3.2.1 Motivation

3.2.2 Structured Monte Carlo

3.2.3 Scenario analysis

3.2.3.1 Correlation breakdown

3.2.3.2 Generating reasonable stress

3.2.3.3 Stress testing in practice

3.2.3.4 Stress testing and historical simulation

3.2.3.5 Asset concentration

3.3 WORST-CASE SCENARIO (WCS)

3.3.1 WCS vs. VaR

3.3.2 A comparison of VaR to WCS

3.3.3 Extensions

3.4 SUMMARY

66. APPENDIX 3.1 DURATION

4 EXTENDING THE VaR APPROACH TO NON-TRADABLE LOANS

4.1 TRADITIONAL APPROACHES TO CREDIT RISK MEASUREMENT

4.1.1 Expert systems

4.1.2 Rating systems

4.1.3 Credit scoring models

4.2 THEORETICAL UNDERPINNINGS: TWO APPROACHES

4.2.1 Options-theoretic structural models of credit risk measurement

4.2.2 Reduced form or intensity-based models of credit risk measurement

4.2.3 Proprietary VaR models of credit risk measurement

4.3 CREDITMETRICS

4.3.1 The distribution of an individual loan’s value

4.3.2 The value distribution for a portfolio of loans

4.3.2.1 Calculating the correlation between equity returns and industry indices for each borrower in the loan portfolio

4.3.2.2 Calculating the correlation between borrower equity returns

4.3.2.3 Solving for joint migration probabilities

4.3.2.4 Valuing each loan across the entire credit migration spectrum

4.3.2.5 Calculating the mean and standard deviation of the normal portfolio value distribution

4.4 ALGORITHMICS’ MARK-TO-FUTURE

4.5 SUMMARY

86. APPENDIX 4.1 CREDITMETRICS: CALCULATING CREDIT VaR USING THE ACTUAL DISTRIBUTION

5 EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS

5.1 TOP-DOWN APPROACHES TO OPERATIONAL RISK MEASUREMENT

5.1.1 Top-down vs. bottom-up models

5.1.2 Data requirements

5.1.3 Top-down models

5.1.3.1 Multi-factor models

5.1.3.2 Income-based models

5.1.3.3 Expense-based models

5.1.3.4 Operating leverage models

5.1.3.5 Scenario analysis

5.1.3.6 Risk profiling models

5.2 BOTTOM-UP APPROACHES TO OPERATIONAL RISK MEASUREMENT

5.2.1 Process approaches

5.2.1.1 Causal networks or scorecards

5.2.1.2 Connectivity models

5.2.1.3 Reliability models

5.2.2 Actuarial approaches

5.2.2.1 Empirical loss distributions

5.2.2.2 Parametric loss distributions

5.2.3 Proprietary operational risk models 31

5.3 HEDGING OPERATIONAL RISK

5.3.1 Insurance

5.3.2 Self-insurance

5.3.3 Hedging using derivatives

5.3.3.1 Catastrophe options

5.3.3.2 Cat bonds

5.3.4 Limitations to operational risk hedging

5.4 SUMMARY

115. APPENDIX 5.1 COPULA FUNCTIONS

6 APPLYING VaR TO REGULATORY MODELS

6.1 BIS REGULATORY MODELS OF MARKET RISK

6.1.1 The standardized framework for market risk

6.1.1.1 Measuring interest rate risk

6.1.1.2 Measuring foreign exchange rate risk

6.1.1.3 Measuring equity price risk

6.1.2 Internal models of market risk

6.2 BIS REGULATORY MODELS OF CREDIT RISK

6.2.1 The Standardized Model for credit risk

6.2.2 The Internal Ratings-Based Models for credit risk

6.2.2.1 The Foundation IRB Approach

6.2.2.2 The Advanced IRB Approach

6.2.3 BIS regulatory models of off-balance sheet credit risk

6.2.4 Assessment of the BIS regulatory models of credit risk

6.3 BIS REGULATORY MODELS OF OPERATIONAL RISK

6.3.1 The Basic Indicator Approach

6.3.2 The Standardized Approach

6.3.3 The Advanced Measurement Approach

6.3.3.1 The internal measurement approach

6.3.3.2 The loss distribution approach

6.3.3.3 The scorecard approach

6.4 SUMMARY

7 VaR: OUTSTANDING RESEARCH

7.1 DATA AVAILABILITY

7.2 MODEL INTEGRATION

7.3 DYNAMIC MODELING

142. NOTES

143. REFERENCES

144. INDEX