The Basel II Risk Parameters

Transcription

1 The Basel II Risk Parameters

2 Bernd Engelmann Robert Rauhmeier (Editors) The Basel II Risk Parameters Estimation, Validation, and Stress Testing With 7 Figures and 58Tables 12

3 Dr. Bernd Engelmann Quanteam Dr. Bernd Engelmann und Særen Gerlach GbR Basaltstraûe Frankfurt Dr. Robert Rauhmeier Dresdner Bank AG Risk Instruments ± Methods Gallusanlage Frankfurt robert.rauhmeier@dresdner-bank.com ISBN-10 ISBN Springer Berlin Heidelberg New York Springer Berlin Heidelberg New York Cataloging-in-Publication Data Library of Congress Control Number: This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com Springer Berlin Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Softcover-Design: Design & Production, Heidelberg SPIN / ± Printed on acid-free paper

4 Preface In the last decade the banking industry has experienced a significant development in the understanding of credit risk. Refined methods were proposed concerning the estimation of key risk parameters like default probabilities. Further, a large volume of literature on the pricing and measurement of credit risk in a portfolio context has evolved. This development was partly reflected by supervisors when they agreed on the new revised capital adequacy framework, Basel II. Under Basel II, the level of regulatory capital depends on the risk characteristics of each credit while a portfolio context is still neglected. The focus of this book is on the estimation and validation of the three key Basel II risk parameters, probability of default (PD), loss given default (LGD), and exposure at default (EAD). Since the new regulatory framework will become operative in January 2007 (at least in Europe), many banks are in the final stages of implementation. Many questions have arisen during the implementation phase and are discussed by practitioners, supervisors, and academics. A best practice approach has to be formed and will be refined in the future even beyond With this book we aim to contribute to this process. Although the book is inspired by the new capital framework, we hope that it is valuable in a broader context. The three risk parameters are central inputs to credit portfolio models or credit pricing algorithms and their correct estimation is therefore essential for internal bank controlling and management. This is not a book about the Basel II framework. There is already a large volume of literature explaining the new regulation at length. Rather, we attend to the current state-of-the-art of quantitative and qualitative approaches. The book is a combination of coordinated stand-alone articles, arranged into fifteen chapters so that each chapter can be read exclusively. The authors are all experts from science, supervisory authorities, and banking practice. The book is divided into three main parts: Estimation techniques for the parameters PD, LGD and EAD, validation of these parameters, and stress testing. The first part begins with an overview of the popular and established methods for estimating PD. Chapter II focuses on methods for PD estimation for small and medium sized corporations while Chapter III treats the PD estimation for the retail segment. Chapters IV and V deal with those segments with only a few or even no default data, as it is often the case in the large corporate, financial institutions, or sovereign segment. Chapter IV illustrates how PD can be estimated with the shadow rating approach while Chapter V uses techniques from probability theory. Chapter VI describes how PDs and Recovery Rates could be estimated under considerations of systematic and idiosyncratic risk factors simultaneously. This is a perfect changeover to the chapters VII to X dealing with LGD and EAD estimation which is quite new in practice compared to ratings and PD estimation. Chap-

5 vi Preface ter VII describes how LGD could be modelled in a point-in-time framework as a function of risk drivers, supported by an empirical study on bond data. Chapter VIII provides a general survey of LGD estimation from a practical point of view. Chapters IX and X are concerned with the modelling of EAD. Chapter IX provides a general overview of EAD estimation techniques while Chapter X focuses on the estimation of EAD for facilities with explicit limits. The second part of the book consists of four chapters about validation and statistical back-testing of rating systems. Chapter XI deals with the perspective of the supervisory authorities and gives a glance as to what is expected when rating systems will be used under the Basel II framework. Chapter XII has a critical discussion on measuring the discriminatory power of rating systems. Chapter XIII gives an overview of statistical tests for the dimension calibration, i.e. the accuracy of PD estimations. In Chapter XIV these methods are enhanced by techniques of Monte-Carlo-Simulations which allows e.g. for integration of correlation assumptions as is also illustrated within a back-testing study on a real-life rating data sample. The final part consists of Chapter XV, which is on stress testing. The purpose of stress testing is to detect limitations of models for the risk parameters and to analyse effects of (extreme) worse scenarios in the future on a bank s portfolio. Concepts and implementation strategies of stress test are explained and a simulation study reveals amazing effects of stress scenarios when calculating economic capital with a portfolio model. All articles set great value on practical applicability and mostly include empirical studies or work with examples. Therefore we regard this book as a valuable contribution towards modern risk management in every financial institution, whereas we steadily keep track on the requirements of Basel II. The book is addressed to risk managers, rating analyst and in general quantitative analysts who work in the credit risk area or on regulatory issues. Furthermore, we target internal auditors and supervisors who have to evaluate the quality of rating systems and risk parameter estimations. We hope that this book will deepen their understanding and will be useful for their daily work. Last but not least we hope this book will also be of interest to academics or students in finance or economics who want to get an overview of the state-of-the-art of a currently important topic in the banking industry. Finally, we have to thank all the people who made this book possible. Our sincere acknowledgements go to all the contributors of this book for their work, their enthusiasm, their reliability, and their cooperation. We know that most of the writing had to be done in valuable spare time. We are glad that all of them were willing to make such sacrifices for the sake of this book. Special thank goes to Walter Gruber for bringing us on the idea to edit this book. We are grateful to Martina Bihn from Spinger-Verlag who welcomed our idea for this book and supported our work on it.

6 Preface vii We thank Dresdner Bank AG, especially Peter Gassmann and Dirk Thomas, and Quanteam AG for supporting our book. Moreover we are grateful to all our colleagues and friends who agreed to work as referees or discussion partners. Finally we would like to thank our families for their continued support and understanding. Frankurt am Main Bernd Engelmann Robert Rauhmeier June 2006

7 Contents I. Statistical Methods to Develop Rating Models...1 Evelyn Hayden and Daniel Porath 1. Introduction Statistical Methods for Risk Classification Regression Analysis Discriminant Analysis Logit and Probit Models Panel Models Hazard Models Neural Networks 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 IRBA Minimum Requirements Rating System Design Rating Dimensions...30

8 x Contents 3.3. Risk Drivers Risk Quantification Special Requirements for Scoring Models Methods for Estimating Scoring Models Summary References IV. The Shadow Rating Approach Experience from Banking Practice 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 References V. Estimating Probabilities of Default for Low Default Portfolios 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

9 Contents xi 6. Potential Extension: The Multi-period case Potential Applications Open Issues Conclusions...98 References...99 Appendix A Appendix B VI. A Multi-Factor Approach for Systematic Default and Recovery Risk Daniel Rösch 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 Estimation Results Implications for Economic and Regulatory Capital Discussion References Appendix: Results of Monte-Carlo Simulations VII. Modelling Loss Given Default: A Point in Time -Approach Alfred Hamerle, Michael Knapp, Nicole Wildenauer 1. Introduction Statistical Modelling Empirical Analysis The Data Results Conclusions References Appendix: Macroeconomic Variables VIII. Estimating Loss Given Default Experiences from Banking Practice Christian Peter 1. Introduction LGD Estimates in Risk Management Basel II 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

10 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 References IX. Overview of EAD Estimation Concepts 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 References X. EAD Estimates for Facilities with Explicit Limits 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

11 Contents xiii 7.2. Estimation Procedures 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 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 References XII. Measures of a Rating s Discriminative Power Applications and Limitations 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 References Appendix A. Proof of (2) Appendix B. Proof of (7) XIII. Statistical Approaches to PD Validation Stefan Blochwitz, Marcus R. W. Martin, and Carsten S. Wehn 1. Introduction PDs, Default Rates, and Rating Philosophy...289

12 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 References XIV. PD-Validation Experience from Banking Practice 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- 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 Jan Conclusion References Appendix A Appendix B XV. Development of Stress Tests for Credit Portfolios Volker Matthias Gundlach 1. Introduction The Purpose of Stress Testing Regulatory Requirements Risk Parameters for Stress Testing Evaluating Stress Tests

13 Contents xv 6. Classifying Stress Tests Conducting Stress Tests Uniform Stress Tests Sensitivity Analysis for Risk Factors Scenario Analysis Examples Conclusion References Contributors Index...373