book

The Analytics of Risk Model Validation

by George A. Christodoulakis, Stephen Satchell

November 2007

Intermediate to advanced

216 pages

7h 20m

English

Academic Press

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Cover image
Title page
Table of Contents
Copyright page
About the editors
About the contributors
Preface
1: Determinants of small business default*
Abstract1 Introduction2 Data, methodology and summary statistics3 Empirical results of small business default4 Conclusion
2: Validation of stress testing models
Abstract1 Why stress test?2 Stress testing basics3 Overview of validation approaches4 Subsampling tests5 Ideal scenario validation6 Scenario validation7 Cross-segment validation8 Back-casting9 Conclusions
3: The validity of credit risk model validation methods*
Abstract1 Introduction2 Measures of discriminatory power3 Uncertainty in credit risk model validation4 Confidence interval for ROC5 Bootstrapping6 Optimal rating combinations7 Concluding remarks

4: A moments-based procedure for evaluating risk forecasting models
Abstract1 Introduction2 Preliminary analysis3 The likelihood ratio test4 A moments test of model adequacy5 An illustration6 Conclusions7 AcknowledgementsAppendix1 Error distribution2 Two-piece normal distribution3 t-Distribution4 Skew-t distribution
5: Measuring concentration risk in credit portfolios
Abstract1 Concentration risk and validation2 Concentration risk and the IRB model3 Measuring name concentration4 Measuring sectoral concentration5 Numerical example6 Future challenges of concentration risk measurement7 SummaryAppendix A.1 IRB risk weight functions and concentration riskAppendix A.2 Factor surface for the diversification factorAppendix A.3
6: A Simple method for regulators to cross-check operational risk loss models for banks
Abstract1 Introduction2 Background3 Cross-checking procedure4 Justification of our approach5 Justification for a lower bound using the lognormal distribution6 Conclusion
7: Of the credibility of mapping and benchmarking credit risk estimates for internal rating systems
Abstract1 Introduction2 Why does the portfolio’s structure matter?3 Credible credit ratings and credible credit risk estimates4 An empirical illustration5 Credible mapping6 Conclusions7 AcknowledgementsAppendix
8: Analytic models of the ROC Curve: Applications to credit rating model validation
Abstract1 Introduction2 Theoretical implications and applications3 Choices of distributions4 Performance evaluation on the AUROC estimation with simulated data5 Summary6 Conclusions7 AcknowledgementsAppendix
9: The validation of equity portfolio risk models
Abstract1 Linear factor models2 Building a time series model3 Building a statistical factor model4 Building models with known beta’s5 Forecast construction and evaluation6 Diagnostics7 Time horizons and data frequency8 The residuals9 Monte Carlo procedures10 Conclusions
10: Dynamic risk analysis and risk model evaluation
Abstract1 Introduction2 Volatility over time and the cumulative variance3 Beta over time and cumulative covariance4 Dynamic risk model evaluation5 Summary
11: Validation of internal rating systems and PD estimates
Abstract1 Introduction2 Regulatory background3 Statistical background4 Monotonicity of conditional PDs5 Discriminatory power of rating systems6 Calibration of rating systems7 Conclusions
Index

Content preview from The Analytics of Risk Model Validation

Validation of internal rating systems and PD estimates*

Dirk Tasche^†^† Fitch Ratings Ltd., London, United Kingdom.

Abstract

Based on the theoretical binary classification framework, the notions of discriminatory power of a rating system and calibration of PD (probability of default) estimates are introduced. A variety of tools for measuring and testing discriminatory power and for testing correct calibration is presented.

1 Introduction

This chapter elaborates on the validation requirements for rating systems and probabilities of default (PDs) that were introduced with the New Capital Standards (commonly called ‘Basel II’, cf. BCBS, 2004). We start in Section 2 with some introductory remarks on the topics and approaches that will be discussed later ...

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