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

Preface

Contents

I. Statistical Methods to Develop Rating Models

1. Introduction

2. Statistical Methods for Risk Classification

3. Regression Analysis

4. Discriminant Analysis

5. Logit and Probit Models

6. Panel Models

7. Hazard Models

8. Neural Networks

9. Decision Trees

10. Statistical Models and Basel II

References

II. Estimation of a Rating Model for Corporate Exposures

1. Introduction

2. Model Selection

3. The Data Set

4. Data Processing

4.1. Data Cleaning

4.2. Calculation of Financial Ratios

4.3. Test of Linearity Assumption

5. Model Building

5.1. Pre-selection of Input Ratios

5.2. Derivation of the Final Default Prediction Model

5.3. Model Validation

6. Conclusions

References

III. Scoring Models for Retail Exposures

1. Introduction

2. The Concept of Scoring

2.1. What is Scoring?

2.2. Classing and Recoding

2.3. Different Scoring Models

3. Scoring and the IRBA Minimum Requirements

3.1. Rating System Design

3.2. Rating Dimensions

3.3. Risk Drivers

3.4. Risk Quantification

3.5. Special Requirements for Scoring Models

4. Methods for Estimating Scoring Models

5. Summary

References

IV. The Shadow Rating Approach – Experience from Banking Practice

1. Introduction

2. Calibration of External Ratings

2.1. Introduction

2.2. External Rating Agencies and Rating Types

2.3. Definitions of the Default Event and Default Rates

2.4. Sample for PD Estimation

2.5. PD Estimation Techniques

2.6. Adjustments

2.7. Point-in-Time Adaptation

3. Sample Construction for the SRA Model

3.1. Introduction

3.2. Sample Types

3.3. External PDs and Default Indicator

3.4. Weighting Observations

3.5. Correlated Observations

4. Univariate Risk Factor Analysis

4.1. Introduction

4.2. Discriminatory Power

4.3. Transformation

4.4. Representativeness

4.5. Missing Values

4.6. Summary

5. Multi-factor Model and Validation

5.1. Introduction

5.2. Model Selection

5.3. Model Assumptions

5.4. Measuring Influence

5.5. Manual Adjustments and Calibration

5.6. Two-step Regression

5.7. Corporate Groups and Sovereign Support

5.8. Validation

6. Conclusions

References

V. Estimating Probabilities of Default for Low Default Portfolios

1. Introduction

2. Example: No Defaults, Assumption of Independence

3. Example: Few Defaults, Assumption of Independence

4. Example: Correlated Default Events

5. Potential Extension: Calibration by Scaling Factors

6. Potential Extension: The Multi-period case

7. Potential Applications

8. Open Issues

9. Conclusions

References

Appendix A

Appendix B

VI. A Multi-Factor Approach for Systematic Default and Recovery Risk1

1. Modelling Default and Recovery Risk

2. Model and Estimation

2.1. The Model for the Default Process

2.2. The Model for the Recovery

2.3. A Multi-Factor Model Extension

2.4. Model Estimation

3. Data and Results

3.1. The Data

3.2. Estimation Results

4. Implications for Economic and Regulatory Capital

5. Discussion

References

Appendix: Results of Monte-Carlo Simulations

VII. Modelling Loss Given Default: A “Point in Time”- Approach

1. Introduction

2. Statistical Modelling

3. Empirical Analysis

3.1. The Data

3.2. Results

4. Conclusions

References

Appendix: Macroeconomic variables

VIII. Estimating Loss Given Default – Experiences from Banking Practice

1. Introduction

2. LGD Estimates in Risk Management

2.1. Basel II Requirements on LGD Estimates – a Short Survey

2.2. LGD in Internal Risk Management and Other Applications

3. Definition of Economic Loss and LGD

4. A Short Survey of Different LGD Estimation Methods

5. A Model for Workout LGD

6. Direct Estimation Approaches for LGD

6.1. Collecting Loss Data – the Credit Loss Database

6.2. Model Design and Estimation

7. LGD Estimation for Defaulted Exposures

8. Concluding Remarks

References

IX. Overview of EAD Estimation Concepts

1. EAD Estimation from a Regulatory Perspective

1.1. Definition of Terms

1.2. Regulatory Prescriptions Concerning the EAD Estimation

1.3. Delimitation to Other Loss Parameters

1.4. EAD Estimation for Derivative Products

2. Internal Methods of EAD Estimation

2.1. Empirical Models

2.2. Internal Approaches for EAD Estimation for Derivative Products

3. Conclusion

References

X. EAD Estimates for Facilities with Explicit Limits

1. Introduction

2. Definition of Realised Conversion Factors

3. How to Obtain a Set of Realised Conversion Factors

3.1. Fixed Time Horizon

3.2. Cohort Method

3.3. Variable Time Horizon

4. Data Sets (RDS) for Estimation Procedures

4.1. Structure and Scope of the Reference Data Set

4.2. Data Cleaning

4.3. EAD Risk Drivers

5. EAD Estimates

5.1. Relationship Between Observations in the RDS and the Current Portfolio

5.2. Equivalence between EAD Estimates and CF Estimates

5.3. Modelling Conversion Factors from the Reference Data Set

5.4. LEQ = Constant

5.5. Usage at Default Method with CCF = Constant (Simplified Momentum Method):

6. How to Assess the Optimality of the Estimates

6.1. Type of Estimates

6.2. A Suitable Class of Loss Functions

6.3. The Objective Function

7. Example 1

7.1. RDS

7.2. Estimation Procedures

8. Summary and Conclusions

References

Appendix A. Equivalence Between two Minimisation Problems

Appendix B. Optimal Solutions of Certain Regression and Optimization Problems

Appendix C. Diagnostics of Regressions Models

Appendix D. Abbreviations

XI. Validation of Banks’ Internal Rating Systems - A Supervisory Perspective

1. Basel II and Validating IRB Systems

1.1. Basel’s New Framework (Basel II)

1.2. Some Challenges

1.3. Provisions by the BCBS

2. Validation of Internal Rating Systems in Detail

2.1. Component-based Validation

2.2. Result-based Validation

2.3. Process-based Validation

3. Concluding Remarks

References

XII. Measures of a Rating’s Discriminative Power – Applications and Limitations

1. Introduction

2. Measures of a Rating System’s Discriminative Power

2.1. Cumulative Accuracy Profile

2.2. Receiver Operating Characteristic

2.3. Extensions

3. Statistical Properties of AUROC

3.1. Probabilistic Interpretation of AUROC

3.2. Computing Confidence Intervals for AUROC

3.3. Testing for Discriminative Power

3.4. Testing for the Difference of two AUROCs

4. Correct Interpretation of AUROC

References

Appendix A. Proof of (2)

Appendix B. Proof of (7)

XIII. Statistical Approaches to PD Validation

1. Introduction

2. PDs, Default Rates, and Rating Philosophy

3. Tools for Validating PDs

3.1. Statistical Tests for a Single Time Period

3.2. Statistical Multi-period Tests

3.3. Discussion and Conclusion

4. Practical Limitations to PD Validation

References

XIV. PD-Validation – Experience from Banking Practice

1. Introduction

2. Rating Systems in Banking Practice

2.1. Definition of Rating Systems

2.2. Modular Design of Rating Systems

2.3. Scope of Rating Systems

2.4. Rating Scales and Master Scales

2.5. Parties Concerned by the Quality of Rating Systems

3. Statistical Framework

4. Central Statistical Hypothesis Tests Regarding Calibration

4.1. Binomial Test

4.1.2. Normal Approximation of the Binomial Test

4.2. Spiegelhalter Test (SPGH)

4.3. Hosmer-Lemeshow-Test (HSLS)

4.4. A Test for Comparing Two Rating Systems: The Redelmeier Test

5. The Use of Monte-Carlo Simulation Technique

5.1. Monte-Carlo-Simulation and Test Statistic: Correction of Finite Sample Size and Integration of Asset Correlation

5.2. Assessing the Test Power by Means of Monte-Carlo-Simulation

6. Creating Backtesting Data Sets – The Concept of the Rolling 12- Month- Windows

7. Empirical Results

7.1. Data Description

7.2. The First Glance: Forecast vs. Realised Default Rates

7.3. Results of the Hypothesis Tests for all Slices

7.4. Detailed Analysis of Slice ‘Jan2005’

8. Conclusion

References

Appendix A

Appendix B

XV. Development of Stress Tests for Credit Portfolios

1. Introduction

2. The Purpose of Stress Testing

3. Regulatory Requirements

4. Risk Parameters for Stress Testing

5. Evaluating Stress Tests

6. Classifying Stress Tests

7. Conducting Stress Tests

7.1. Uniform Stress Tests

7.2. Sensitivity Analysis for Risk Factors

7.3. Scenario Analysis

8. Examples

9. Conclusion

References

Contributors

Index

Contributors

Index