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The Basel II Risk Parameters - Estimation, Validation, and Stress Testing

of: Bernd Engelmann, Robert Rauhmeier

Springer-Verlag, 2006

ISBN: 9783540330875 , 376 Pages

Format: PDF, Read online

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The Basel II Risk Parameters - Estimation, Validation, and Stress Testing


 

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