The Analytics of Risk Model Validation (Quantitative Finance)

The Analytics of Risk Model Validation......Page 4
Copyright Page......Page 5
Contents......Page 6
About the editors......Page 8
About the contributors......Page 10
Preface......Page 14
1. Introduction......Page 16
2. Data, methodology and summary statistics......Page 18
3. Empirical results of small business default......Page 21
4. Conclusion......Page 25
Notes......Page 26
1. Why stress test?......Page 28
2. Stress testing basics......Page 29
3. Overview of validation approaches......Page 32
4. Subsampling tests......Page 33
5. Ideal scenario validation......Page 37
6. Scenario validation......Page 38
8. Back-casting......Page 39
References......Page 40
1. Introduction......Page 42
2. Measures of discriminatory power......Page 43
3. Uncertainty in credit risk model validation......Page 46
4. Confidence interval for ROC......Page 48
6. Optimal rating combinations......Page 56
References......Page 57
1. Introduction......Page 60
3. The likelihood ratio test......Page 62
4. A moments test of model adequacy......Page 63
5. An illustration......Page 66
6. Conclusions......Page 68
References......Page 70
Notes......Page 71
1. Error distribution......Page 72
4. Skew-t distribution......Page 73
1. Concentration risk and validation......Page 74
2. Concentration risk and the IRB model......Page 75
3. Measuring name concentration......Page 78
4. Measuring sectoral concentration......Page 80
5. Numerical example......Page 84
6. Future challenges of concentration risk measurement......Page 86
7. Summary......Page 88
References......Page 89
Notes......Page 90
Appendix A.1: IRB risk weight functions and concentration risk......Page 91
Appendix A.2: Factor surface for the diversification factor......Page 92
Appendix A.3......Page 93
1. Introduction......Page 94
2. Background......Page 96
3. Cross-checking procedure......Page 97
4. Justification of our approach......Page 99
5. Justification for a lower bound using the lognormal distribution......Page 101
6. Conclusion......Page 104
References......Page 105
1. Introduction......Page 106
2. Why does the portfolio’s structure matter?......Page 107
3. Credible credit ratings and credible credit risk estimates......Page 109
4. An empirical illustration......Page 112
5. Credible mapping......Page 117
References......Page 121
2. Proof of the credibility fundamental relation......Page 122
3. Mixed Gamma–Poisson distribution and negative binomial......Page 124
4. Calculation of the Bühlmann credibility estimate under the Gamma–Poisson model......Page 125
5. Calculation of accuracy ratio......Page 126
1. Introduction......Page 128
2. Theoretical implications and applications......Page 129
3. Choices of distributions......Page 135
4. Performance evaluation on the AUROC estimation with simulated data......Page 138
5. Summary......Page 144
7. Acknowledgements......Page 145
1. The properties of AUROC for normally distributed sample......Page 146
Abstract......Page 150
1. Linear factor models......Page 151
2. Building a time series model......Page 152
3. Building a statistical factor model......Page 153
4. Building models with known beta’s......Page 155
5. Forecast construction and evaluation......Page 157
6. Diagnostics......Page 158
7. Time horizons and data frequency......Page 160
8. The residuals......Page 161
10. Conclusions......Page 162
References......Page 163
1. Introduction......Page 164
2. Volatility over time and the cumulative variance......Page 166
3. Beta over time and cumulative covariance......Page 174
4. Dynamic risk model evaluation......Page 179
5. Summary......Page 182
References......Page 183
1. Introduction......Page 184
2. Regulatory background......Page 185
3. Statistical background......Page 187
4. Monotonicity of conditional PDs......Page 194
5. Discriminatory power of rating systems......Page 197
6. Calibration of rating systems......Page 206
Notes......Page 211
Index......Page 212