Understanding Market, Credit, and Operational Risk: The Value at Risk Approach

LIST OF FIGURES......Page 15
LIST OF TABLES......Page 17
PREFACE......Page 19
LIST OF ABBREVIATIONS......Page 21
1 INTRODUCTION TO VALUE AT RISK (VaR)......Page 24
1.1 ECONOMICS UNDERLYING VaR MEASUREMENT......Page 25
1.1.1 What is VaR?......Page 27
1.1.2 Calculating VaR......Page 29
1.1.3 The assumptions behind VaR calculations......Page 31
1.1.4 Inputs into VaR calculations......Page 33
1.2 DIVERSIFICATION AND VaR......Page 36
1.2.1 Factors affecting portfolio diversification......Page 39
1.2.2 Decomposing volatility into systematic and idiosyncratic risk......Page 40
1.2.3 Diversification: Words of caution – the case of long-term capital management (LTCM)......Page 41
2 QUANTIFYING VOLATILITY IN VaR MODELS......Page 44
2.1.1 Revisiting the assumptions......Page 45
2.1.2 The distribution of interest rate changes......Page 46
2.1.3 Fat tails......Page 48
2.1.4 Explaining fat tails......Page 49
2.1.5 Effects of volatility changes......Page 52
2.1.6 Can (conditional) normality be salvaged?......Page 54
2.1.7 Normality cannot be salvaged......Page 57
2.2 VaR ESTIMATION APPROACHES......Page 58
2.2.2 Historical standard deviation......Page 59
2.2.3 Implementation considerations......Page 61
2.2.4 Exponential smoothing – RiskMetrics™ volatility......Page 63
2.2.4.1 The optimal smoother lambda......Page 66
2.2.4.2 Adaptive volatility estimation......Page 67
2.2.4.4 GARCH......Page 68
2.2.5.1 Historical simulation......Page 71
2.2.5.2 Multivariate density estimation......Page 74
2.2.6 A comparison of methods......Page 77
2.2.7 The hybrid approach......Page 79
2.3 RETURN AGGREGATION AND VaR......Page 82
2.4 IMPLIED VOLATILITY AS A PREDICTOR OF FUTURE VOLATILITY......Page 85
2.5 LONG HORIZON VOLATILITY AND VaR......Page 89
2.6 MEAN REVERSION AND LONG HORIZON VOLATILITY......Page 92
2.7 CORRELATION MEASUREMENT......Page 94
APPENDIX 2.1 BACKTESTING METHODOLOGY AND RESULTS......Page 97
3.1 THE VaR OF DERIVATIVES – PRELIMINARIES......Page 105
3.1.1 Linear derivatives......Page 106
3.1.3 Approximating the VaR of derivatives......Page 109
3.1.4 Fixed income securities with embedded optionality......Page 116
3.1.5 “Delta normal” vs. full-revaluation......Page 118
3.2.1 Motivation......Page 120
3.2.2 Structured Monte Carlo......Page 121
3.2.3.1 Correlation breakdown......Page 124
3.2.3.2 Generating reasonable stress......Page 126
3.2.3.3 Stress testing in practice......Page 127
3.2.3.4 Stress testing and historical simulation......Page 129
3.2.3.5 Asset concentration......Page 130
3.3.1 WCS vs. VaR......Page 133
3.3.2 A comparison of VaR to WCS......Page 134
3.3.3 Extensions......Page 135
3.4 SUMMARY......Page 136
APPENDIX 3.1 DURATION......Page 137
4 EXTENDING THE VaR APPROACH TO NON-TRADABLE LOANS......Page 142
4.1 TRADITIONAL APPROACHES TO CREDIT RISK MEASUREMENT......Page 143
4.1.1 Expert systems......Page 144
4.1.2 Rating systems......Page 145
4.1.3 Credit scoring models......Page 147
4.2.1 Options-theoretic structural models of credit risk measurement......Page 151
4.2.2 Reduced form or intensity-based models of credit risk measurement......Page 155
4.3.1 The distribution of an individual loan’s value......Page 161
4.3.2 The value distribution for a portfolio of loans......Page 166
4.3.2.2 Calculating the correlation between borrower equity returns......Page 167
4.3.2.3 Solving for joint migration probabilities......Page 168
4.3.2.4 Valuing each loan across the entire credit migration spectrum......Page 170
4.3.2.5 Calculating the mean and standard deviation of the normal portfolio value distribution......Page 172
4.4 ALGORITHMICS’ MARK-TO-FUTURE......Page 174
4.5 SUMMARY......Page 176
APPENDIX 4.1 CREDITMETRICS: CALCULATING CREDIT VaR USING THE ACTUAL DISTRIBUTION......Page 178
5 EXTENDING THE VaR APPROACH TO OPERATIONAL RISKS......Page 181
5.1 TOP-DOWN APPROACHES TO OPERATIONAL RISK MEASUREMENT......Page 184
5.1.1 Top-down vs. bottom-up models......Page 185
5.1.2 Data requirements......Page 186
5.1.3.1 Multi-factor models......Page 188
5.1.3.2 Income-based models......Page 189
5.1.3.5 Scenario analysis......Page 190
5.1.3.6 Risk profiling models......Page 191
5.2.1.1 Causal networks or scorecards......Page 193
5.2.1.2 Connectivity models......Page 196
5.2.1.3 Reliability models......Page 198
5.2.2.2 Parametric loss distributions......Page 199
5.2.3 Proprietary operational risk models 31......Page 205
5.3 HEDGING OPERATIONAL RISK......Page 208
5.3.1 Insurance......Page 209
5.3.2 Self-insurance......Page 211
5.3.3 Hedging using derivatives......Page 213
5.3.3.1 Catastrophe options......Page 214
5.3.3.2 Cat bonds......Page 216
5.3.4 Limitations to operational risk hedging......Page 218
APPENDIX 5.1 COPULA FUNCTIONS......Page 219
6 APPLYING VaR TO REGULATORY MODELS......Page 223
6.1.1.1 Measuring interest rate risk......Page 226
6.1.1.2 Measuring foreign exchange rate risk......Page 227
6.1.2 Internal models of market risk......Page 228
6.2 BIS REGULATORY MODELS OF CREDIT RISK......Page 229
6.2.1 The Standardized Model for credit risk......Page 230
6.2.2 The Internal Ratings-Based Models for credit risk......Page 232
6.2.2.1 The Foundation IRB Approach......Page 233
6.2.2.2 The Advanced IRB Approach......Page 237
6.2.3 BIS regulatory models of off-balance sheet credit risk......Page 238
6.2.4 Assessment of the BIS regulatory models of credit risk......Page 241
6.3 BIS REGULATORY MODELS OF OPERATIONAL RISK......Page 244
6.3.1 The Basic Indicator Approach......Page 246
6.3.2 The Standardized Approach......Page 247
6.3.3 The Advanced Measurement Approach......Page 248
6.3.3.1 The internal measurement approach......Page 250
6.3.3.3 The scorecard approach......Page 253
6.4 SUMMARY......Page 254
7.1 DATA AVAILABILITY......Page 256
7.2 MODEL INTEGRATION......Page 257
7.3 DYNAMIC MODELING......Page 258
NOTES......Page 259
REFERENCES......Page 280
INDEX......Page 293