The Basel II Risk Parameters

Transcription

1 Bernd Engelmann Robert Rauhmeier (Editors) The Basel II Risk Parameters Estimation, Validation, and Stress Testing With 7 Figures and 58 Tables 4y Springer

2 I. Statistical Methods to Develop Rating Models 1 Evelyn Hayden and Daniel Porath 1. Introduction 1 2. Statistical Methods for Risk Classification 1 3. Regression Analysis 2 4. Discriminant Analysis 3 5. Logit and Probit Models 4 6. Panel Models 7 7. Hazard Models 8 8. Neural Networks 9 9. Decision Trees Statistical Models and Basel II 11 References 12 II. Estimation of a Rating Model for Corporate Exposures 13 Evelyn Hayden 1. Introduction Model Selection The Data Set Data Processing Data Cleaning Calculation of Financial Ratios Test of Linearity Assumption Model Building Pre-selection of Input Ratios Derivation of the Final Default Prediction Model Model Validation Conclusions 24 References 24 III. Scoring Models for Retail Exposures 25 Daniel Porath 1. Introduction The Concept of Scoring What is Scoring? Classing and Recoding Different Scoring Models Scoring and the 1RBA Minimum Requirements Rating System Design Rating Dimensions 30

3 3.3. Risk Drivers Risk Quantification Special Requirements for Scoring Models Methods for Estimating Scoring Models Summary 36 References 37 IV. The Shadow Rating Approach - Experience from Banking Practice 39 Ulrich Erlenmaier 1. Introduction Calibration of External Ratings Introduction External Rating Agencies and Rating Types Definitions of the Default Event and Default Rates Sample for PD Estimation PD Estimation Techniques Adjustments Point-in-Time Adaptation Sample Construction for the SRA Model External PDs and Default Indicator Univariate Risk Factor Analysis Introduction Discriminatory Power Transformation Representativeness Missing Values Summary Multi-factor Model and Validation Introduction Model Selection Model Assumptions Measuring Influence Manual Adjustments and Calibration Two-step Regression Corporate Groups and Sovereign Support Validation Conclusions 75 References 76 V. Estimating Probabilities of Default for Low Default Portfolios 79 Katja Pluto and Dirk Tasche 1. Introduction Example: No Defaults, Assumption of Independence Example: Few Defaults, Assumption of Independence Example: Correlated Default Events Potential Extension: Calibration by Scaling Factors 89

4 xi 6. Potential Extension: The Multi-period case Potential Applications Open Issues Conclusions 98 References 99 Appendix A 100 Appendix B 102 VI. A Multi-Factor Approach for Systematic Default and Recovery Risk Daniel Rosch and Harald Scheule 1. Modelling Default and Recovery Risk Model and Estimation The Model for the Default Process The Model for the Recovery A Multi-Factor Model Extension Model Estimation Data and Results The Data Ill 3.2. Estimation Results Implications for Economic and Regulatory Capital Discussion 122 References 123 Appendix: Results of Monte-Carlo Simulations 124 VII. Modelling Loss Given Default: A "Point in Time"-Approach 127 Alfred Hamerle, Michael Knapp, Nicole Wildenauer 1. Introduction Statistical Modelling Empirical Analysis The Data Results Conclusions 138 References 139 Appendix: Macroeconomic Variables 140 VIII. Estimating Loss Given Default - Experiences from Banking Practice 143 Christian Peter 1. Introduction LGD Estimates in Risk Management Basel 11 Requirements on LGD Estimates - a Short Survey LGD in Internal Risk Management and Other Applications Definition of Economic Loss and LGD A Short Survey of Different LGD Estimation Methods A Model for Workout LGD 151

5 xii Contents 6. Direct Estimation Approaches for LGD Collecting Loss Data-the Credit Loss Database Model Design and Estimation LGD Estimation for Defaulted Exposures Concluding Remarks 173 References 174 IX. Overview of EAD Estimation Concepts 177 Walter Gruber and Ronny Parchert 1. EAD Estimation from a Regulatory Perspective Definition of Terms Regulatory Prescriptions Concerning the EAD Estimation Delimitation to Other Loss Parameters EAD Estimation for Derivative Products Internal Methods of EAD Estimation Empirical Models Internal Approaches for EAD Estimation for Derivative Products Conclusion 195 References 195 X. EAD Estimates for Facilities with Explicit Limits 197 Gregorio Moral 1. Introduction Definition of Realised Conversion Factors How to Obtain a Set of Realised Conversion Factors Fixed Time Horizon Cohort Method Variable Time Horizon Data Sets (RDS) for Estimation Procedures Structure and Scope of the Reference Data Set Data Cleaning EAD Risk Drivers EAD Estimates Relationship Between Observations in the RDS and the Current Portfolio Equivalence between EAD Estimates and CF Estimates Modelling Conversion Factors from the Reference Data Set LEQ = Constant Usage at Default Method with CCF = Constant (Simplified Momentum Method) How to Assess the Optimality of the Estimates Type of Estimates A Suitable Class of Loss Functions The Objective Function Example RDS 223

6 xiii 7.2. Estimation Procedures Summary and Conclusions 235 References 236 Appendix A. Equivalence between two Minimisation Problems 237 Appendix B. Optimal Solutions of Certain Regression and Optimization Problems 238 Appendix C. Diagnostics of Regressions Models 239 Appendix D. Abbreviations 242 XL Validation of Banks' Internal Rating Systems - A Supervisory Perspective 243 Stefan Blochwitz and Stefan Hohl 1. Basel II and Validating IRB Systems Basel's New Framework (Basel II) Some Challenges Provisions by the BCBS Validation of Internal Rating Systems in Detail Component-based Validation Result-based Validation Process-based Validation Concluding Remarks 261 References 262 XII. Measures of a Rating's Discriminative Power - Applications and Limitations 263 Bernd Engelmann 1. Introduction Measures of a Rating System's Discriminative Power Cumulative Accuracy Profile Receiver Operating Characteristic Extensions Statistical Properties of AUROC Probabilistic Interpretation of AUROC Computing Confidence Intervals for AUROC Testing for Discriminative Power Testing for the Difference of two AUROCs Correct Interpretation of AUROC 283 References 285 Appendix A. Proof of (2) 285 Appendix B. Proof of (7) 286 XIII. Statistical Approaches to PD Validation 289 Stefan Blochwitz, Marcus R. W. Martin, and Carsten S. Wehn 1. Introduction PDs, Default Rates, and Rating Philosophy 289

7 xiv Contents 3. Tools for Validating PDs Statistical Tests for a Single Time Period Statistical Multi-period Tests Discussion and Conclusion Practical Limitations to PD Validation 303 References 305 XIV. PD-Validation - Experience from Banking Practice 307 Robert Rauhmeier 1. Introduction Rating Systems in Banking Practice Definition of Rating Systems Modular Design of Rating Systems Scope of Rating Systems Rating Scales and Master Scales Parties Concerned by the Quality of Rating Systems Statistical Framework Central Statistical Hypothesis Tests Regarding Calibration Binomial Test Spiegelhalter Test (SPGH) Hosmer-Lemeshow-x 2 Test (HSLS) A Test for Comparing Two Rating Systems: The Redelmeier Test The Use of Monte-Carlo Simulation Technique Monte-Carlo-Simulation and Test Statistic: Correction of Finite Sample Size and Integration of Asset Correlation Assessing the Test Power by Means of Monte-Carlo-Simulation Creating Backtesting Data Sets - The Concept of the Rolling 12-Month-Windows Empirical Results Data Description The First Glance: Forecast vs. Realised Default Rates Results of the Hypothesis Tests for all Slices Detailed Analysis of Slice 'Jan2005' Conclusion 341 References 342 Appendix A 344 Appendix B 345 XV. Development of Stress Tests for Credit Portfolios 347 Volker Matthias Gundlach 1. Introduction The Purpose of Stress Testing Regulatory Requirements Risk Parameters for Stress Testing Evaluating Stress Tests 353

8 xv 6. Classifying Stress Tests Conducting Stress Tests Uniform Stress Tests Sensitivity Analysis for Risk Factors Scenario Analysis Examples Conclusion 366 References 368 Contributors 369 Index 373