The Basel II Risk Parameters (eBook)

Preface 5
Contents 9
I. Statistical Methods to Develop Rating Models 16
1. Introduction 16
2. Statistical Methods for Risk Classification 16
3. Regression Analysis 17
4. Discriminant Analysis 18
5. Logit and Probit Models 19
6. Panel Models 22
7. Hazard Models 23
8. Neural Networks 24
9. Decision Trees 25
10. Statistical Models and Basel II 26
References 27
II. Estimation of a Rating Model for Corporate Exposures 28
1. Introduction 28
2. Model Selection 28
3. The Data Set 29
4. Data Processing 30
4.1. Data Cleaning 30
4.2. Calculation of Financial Ratios 31
4.3. Test of Linearity Assumption 32
5. Model Building 34
5.1. Pre-selection of Input Ratios 34
5.2. Derivation of the Final Default Prediction Model 36
5.3. Model Validation 37
6. Conclusions 39
References 39
III. Scoring Models for Retail Exposures 40
1. Introduction 40
2. The Concept of Scoring 41
2.1. What is Scoring? 41
2.2. Classing and Recoding 42
2.3. Different Scoring Models 44
3. Scoring and the IRBA Minimum Requirements 45
3.1. Rating System Design 45
3.2. Rating Dimensions 45
3.3. Risk Drivers 46
3.4. Risk Quantification 46
3.5. Special Requirements for Scoring Models 47
4. Methods for Estimating Scoring Models 47
5. Summary 51
References 52
IV. The Shadow Rating Approach – Experience from Banking Practice 54
1. Introduction 54
2. Calibration of External Ratings 57
2.1. Introduction 57
2.2. External Rating Agencies and Rating Types 58
2.3. Definitions of the Default Event and Default Rates 59
2.4. Sample for PD Estimation 60
2.5. PD Estimation Techniques 61
2.6. Adjustments 62
2.7. Point-in-Time Adaptation 63
3. Sample Construction for the SRA Model 65
3.1. Introduction 65
3.2. Sample Types 66
3.3. External PDs and Default Indicator 69
3.4. Weighting Observations 71
3.5. Correlated Observations 71
4. Univariate Risk Factor Analysis 72
4.1. Introduction 72
4.2. Discriminatory Power 73
4.3. Transformation 74
4.4. Representativeness 77
4.5. Missing Values 78
4.6. Summary 80
5. Multi-factor Model and Validation 81
5.1. Introduction 81
5.2. Model Selection 81
5.3. Model Assumptions 82
5.4. Measuring Influence 85
5.5. Manual Adjustments and Calibration 87
5.6. Two-step Regression 88
5.7. Corporate Groups and Sovereign Support 88
5.8. Validation 89
6. Conclusions 90
References 91
V. Estimating Probabilities of Default for Low Default Portfolios 94
1. Introduction 94
2. Example: No Defaults, Assumption of Independence 96
3. Example: Few Defaults, Assumption of Independence 98
4. Example: Correlated Default Events 101
5. Potential Extension: Calibration by Scaling Factors 104
6. Potential Extension: The Multi-period case 107
7. Potential Applications 112
8. Open Issues 112
9. Conclusions 113
References 114
Appendix A 115
Appendix B 117
VI. A Multi-Factor Approach for Systematic Default and Recovery Risk1 120
1. Modelling Default and Recovery Risk 120
2. Model and Estimation 121
2.1. The Model for the Default Process 121
2.2. The Model for the Recovery 122
2.3. A Multi-Factor Model Extension 123
2.4. Model Estimation 125
3. Data and Results 126
3.1. The Data 126
3.2. Estimation Results 129
4. Implications for Economic and Regulatory Capital 133
5. Discussion 137
References 138
Appendix: Results of Monte-Carlo Simulations 139
VII. Modelling Loss Given Default: A “Point in Time”- Approach 142
1. Introduction 142
2. Statistical Modelling 144
3. Empirical Analysis 146
3.1. The Data 146
3.2. Results 149
4. Conclusions 153
References 154
Appendix: Macroeconomic variables 155
VIII. Estimating Loss Given Default – Experiences from Banking Practice 158
1. Introduction 158
2. LGD Estimates in Risk Management 159
2.1. Basel II Requirements on LGD Estimates – a Short Survey 159
2.2. LGD in Internal Risk Management and Other Applications 160
3. Definition of Economic Loss and LGD 162
4. A Short Survey of Different LGD Estimation Methods 164
5. A Model for Workout LGD 166
6. Direct Estimation Approaches for LGD 168
6.1. Collecting Loss Data – the Credit Loss Database 169
6.2. Model Design and Estimation 171
7. LGD Estimation for Defaulted Exposures 185
8. Concluding Remarks 188
References 189
IX. Overview of EAD Estimation Concepts 192
1. EAD Estimation from a Regulatory Perspective 192
1.1. Definition of Terms 192
1.2. Regulatory Prescriptions Concerning the EAD Estimation 193
1.3. Delimitation to Other Loss Parameters 194
1.4. EAD Estimation for Derivative Products 196
2. Internal Methods of EAD Estimation 199
2.1. Empirical Models 199
2.2. Internal Approaches for EAD Estimation for Derivative Products 201
3. Conclusion 210
References 210
X. EAD Estimates for Facilities with Explicit Limits 212
1. Introduction 212
2. Definition of Realised Conversion Factors 213
3. How to Obtain a Set of Realised Conversion Factors 216
3.1. Fixed Time Horizon 216
3.2. Cohort Method 217
3.3. Variable Time Horizon 218
4. Data Sets (RDS) for Estimation Procedures 220
4.1. Structure and Scope of the Reference Data Set 221
4.2. Data Cleaning 222
4.3. EAD Risk Drivers 226
5. EAD Estimates 228
5.1. Relationship Between Observations in the RDS and the Current Portfolio 228
5.2. Equivalence between EAD Estimates and CF Estimates 228
5.3. Modelling Conversion Factors from the Reference Data Set 229
5.4. LEQ = Constant 232
5.5. Usage at Default Method with CCF = Constant (Simplified Momentum Method): 233
6. How to Assess the Optimality of the Estimates 234
6.1. Type of Estimates 234
6.2. A Suitable Class of Loss Functions 235
6.3. The Objective Function 236
7. Example 1 238
7.1. RDS 238
7.2. Estimation Procedures 243
8. Summary and Conclusions 250
References 251
Appendix A. Equivalence Between two Minimisation Problems 252
Appendix B. Optimal Solutions of Certain Regression and Optimization Problems 253
Appendix C. Diagnostics of Regressions Models 254
Appendix D. Abbreviations 257
XI. Validation of Banks’ Internal Rating Systems - A Supervisory Perspective 258
1. Basel II and Validating IRB Systems 258
1.1. Basel’s New Framework (Basel II) 258
1.2. Some Challenges 259
1.3. Provisions by the BCBS 262
2. Validation of Internal Rating Systems in Detail 265
2.1. Component-based Validation 265
2.2. Result-based Validation 271
2.3. Process-based Validation 274
3. Concluding Remarks 276
References 277
XII. Measures of a Rating’s Discriminative Power – Applications and Limitations 278
1. Introduction 278
2. Measures of a Rating System’s Discriminative Power 280
2.1. Cumulative Accuracy Profile 281
2.2. Receiver Operating Characteristic 283
2.3. Extensions 287
3. Statistical Properties of AUROC 290
3.1. Probabilistic Interpretation of AUROC 290
3.2. Computing Confidence Intervals for AUROC 292
3.3. Testing for Discriminative Power 294
3.4. Testing for the Difference of two AUROCs 295
4. Correct Interpretation of AUROC 298
References 300
Appendix A. Proof of (2) 300
Appendix B. Proof of (7) 301
XIII. Statistical Approaches to PD Validation 304
1. Introduction 304
2. PDs, Default Rates, and Rating Philosophy 304
3. Tools for Validating PDs 306
3.1. Statistical Tests for a Single Time Period 307
3.2. Statistical Multi-period Tests 313
3.3. Discussion and Conclusion 318
4. Practical Limitations to PD Validation 318
References 320
XIV. PD-Validation – Experience from Banking Practice 322
1. Introduction 322
2. Rating Systems in Banking Practice 323
2.1. Definition of Rating Systems 323
2.2. Modular Design of Rating Systems 323
2.3. Scope of Rating Systems 325
2.4. Rating Scales and Master Scales 325
2.5. Parties Concerned by the Quality of Rating Systems 327
3. Statistical Framework 328
4. Central Statistical Hypothesis Tests Regarding Calibration 331
4.1. Binomial Test 332
4.1.2. Normal Approximation of the Binomial Test 333
4.2. Spiegelhalter Test (SPGH) 334
4.3. Hosmer-Lemeshow-Test (HSLS) 335
4.4. A Test for Comparing Two Rating Systems: The Redelmeier Test 336
5. The Use of Monte-Carlo Simulation Technique 338
5.1. Monte-Carlo-Simulation and Test Statistic: Correction of Finite Sample Size and Integration of Asset Correlation 338
5.2. Assessing the Test Power by Means of Monte-Carlo-Simulation 344
6. Creating Backtesting Data Sets – The Concept of the Rolling 12- Month- Windows 348
7. Empirical Results 351
7.1. Data Description 351
7.2. The First Glance: Forecast vs. Realised Default Rates 352
7.3. Results of the Hypothesis Tests for all Slices 352
7.4. Detailed Analysis of Slice ‘Jan2005’ 354
8. Conclusion 356
References 357
Appendix A 359
Appendix B 360
XV. Development of Stress Tests for Credit Portfolios 362
1. Introduction 362
2. The Purpose of Stress Testing 363
3. Regulatory Requirements 364
4. Risk Parameters for Stress Testing 366
5. Evaluating Stress Tests 368
6. Classifying Stress Tests 369
7. Conducting Stress Tests 373
7.1. Uniform Stress Tests 373
7.2. Sensitivity Analysis for Risk Factors 375
7.3. Scenario Analysis 375
8. Examples 378
9. Conclusion 381
References 383
Contributors 384
Index 388
Contributors 384
Index 388