In the last decade rating-based models have become very popular in credit risk management. These systems use the rating of a company as the decisive variable to evaluate the default risk of a bond or loan. The popularity is due to the straightforwardness of the approach, and to the upcoming new capital accord (Basel II), which allows banks to base their capital requirements on internal as well as external rating systems. Because of this, sophisticated credit risk models are being developed or demanded by banks to assess the risk of their credit portfolio better by recognizing the different underlying sources of risk. As a consequence, not only default probabilities for certain rating categories but also the probabilities of moving from one rating state to another are important issues in such models for risk management and pricing.
It is widely accepted that rating migrations and default probabilities show significant variations through time due to macroeconomics conditions or the business cycle. These changes in migration behavior may have a substantial impact on the value-at-risk (VAR) of a credit portfolio or the prices of credit derivatives such as collateralized debt obligations (D+CDOs). In Rating Based Modeling of Credit Risk the authors develop a much more sophisticated analysis of migration behavior. Their contribution of more sophisticated techniques to measure and forecast changes in migration behavior as well as determining adequate estimators for transition matrices is a major contribution to rating based credit modeling.
- Internal ratings-based systems are widely used in banks to calculate their value-at-risk (VAR) in order to determine their capital requirements for loan and bond portfolios under Basel II
- One aspect of these ratings systems is credit migrations, addressed in a systematic and comprehensive way for the first time in this book
- The book is based on in-depth work by Trueck and Rachev
Inhaltsverzeichnis
1;Front Cover;1 2;Rating Based Modeling of Credit Risk;4 3;Copyright Page;5 4;Table of Contents;8 5;Preface;12 6;Chapter 1. Introduction: Credit Risk Modeling, Ratings, and Migration Matrices;14 6.1;1.1 Motivation;14 6.2;1.2 Structural and Reduced Form Models;15 6.3;1.3 Basel II, Scoring Techniques, and Internal Rating Systems;16 6.4;1.4 Rating Based Modeling and the Pricing of Bonds;17 6.5;1.5 Stability of Transition Matrices, Conditional Migrations, and Dependence;18 6.6;1.6 Credit Derivative Pricing;19 6.7;1.7 Chapter Outline;20 7;Chapter 2. Rating and Scoring Techniques;24 7.1;2.1 Rating Agencies, Rating Processes, and Factors;24 7.1.1;2.1.1 The Rating Process;27 7.1.2;2.1.2 Credit Rating Factors;29 7.1.3;2.1.3 Types of Rating Systems;30 7.2;2.2 Scoring Systems;30 7.3;2.3 Discriminant Analysis;32 7.4;2.4 Logit and Probit Models;34 7.4.1;2.4.1 Logit Models;35 7.4.2;2.4.2 Probit Models;36 7.5;2.5 Model Evaluation: Methods and Difficulties;38 7.5.1;2.5.1 Model Performance and Benchmarking;38 7.5.2;2.5.2 Model Accuracy, Type I and II Errors;42 8;Chapter 3. The New Basel Capital Accord;44 8.1;3.1 Overview;44 8.1.1;3.1.1 The First PillarMinimum Capital Requirement;46 8.1.2;3.1.2 The Second PillarSupervisory Review Process;48 8.1.3;3.1.3 The Third PillarMarket Discipline;48 8.2;3.2 The Standardized Approach;49 8.2.1;3.2.1 Risk Weights for Sovereigns and for Banks;49 8.2.2;3.2.2 Risk Weights for Corporates;52 8.2.3;3.2.3 Maturity;52 8.2.4;3.2.4 Credit Risk Mitigation;53 8.3;3.3 The Internal Ratings Based Approach;54 8.3.1;3.3.1 Key Elements and Risk Components;54 8.3.2;3.3.2 Derivation of the Benchmark Risk Weight Function;55 8.3.3;3.3.3 Asset Correlation;59 8.3.4;3.3.4 The Maturity Adjustment;61 8.3.5;3.3.5 Expected, Unexpected Losses and the Required Capital;63 8.4;3.4 Summary;63 9;Chapter 4. Rating Based Modeling;66 9.1;4.1 Introduction;66 9.2;4.2 Reduced Form and Intensity Models;67 9.2.1;4.2.1 The Model by Jarrow and Turnbull (1995);72 9.2.2;4.2.2 The Model Suggest
ed by Madan and Unal (1998);73 9.2.3;4.2.3 The Model Suggested by Lando (1998);74 9.2.4;4.2.4 The Model of Duffie and Singleton (1999);76 9.3;4.3 The CreditMetrics Model;76 9.4;4.4 The CreditRisk+ Model;81 9.4.1;4.4.1 The First Modeling Approach;81 9.4.2;4.4.2 Modeling Severities;82 9.4.3;4.4.3 Shortcomings of the First Modeling Approach;84 9.4.4;4.4.4 Extensions in the CR+ Model;85 9.4.5;4.4.5 Allocating Obligors to One of Several Factors;85 9.4.6;4.4.6 The pgf for the Number of Defaults;86 9.4.7;4.4.7 The pgf for the Default Loss Distribution;88 9.4.8;4.4.8 Generalization of Obligor Allocation;88 9.4.9;4.4.9 The Default Loss Distribution;89 10;Chapter 5. Migration Matrices and the Markov Chain Approach;90 10.1;5.1 The Markov Chain Approach;90 10.1.1;5.1.1 Generator Matrices;91 10.2;5.2 Discrete Versus Continuous-Time Modeling;93 10.2.1;5.2.1 Some Conditions for the Existence of a Valid Generator;99 10.3;5.3 Approximation of Generator Matrices;101 10.3.1;5.3.1 The Method Proposed by Jarrow, Lando, and Turnbull (1997);101 10.3.2;5.3.2 Methods Suggested by Israel, Rosenthal,and Wei (2000);102 10.4;5.4 Simulating Credit Migrations;105 10.4.1;5.4.1 Time-Discrete Case;105 10.4.2;5.4.2 Time-Continuous Case;106 10.4.3;5.4.3 Nonparametric Approach;107 11;Chapter 6. Stability of Credit Migrations;110 11.1;6.1 Credit Migrations and the Business Cycle;110 11.2;6.2 The Markov Assumptions and Rating Drifts;115 11.2.1;6.2.1 Likelihood Ratio Tests;116 11.2.2;6.2.2 Rating Drift;117 11.2.3;6.2.3 An Empirical Study;118 11.3;6.3 Time Homogeneity of Migration Matrices;122 11.3.1;6.3.1 Tests Using the Chi-Square Distance;123 11.3.2;6.3.2 Eigenvalues and Eigenvectors;123 11.4;6.4 Migration Behavior and Effects on Credit VaR;126 12;Chapter 7. Measures for Comparison of Transition Matrices;142 12.1;7.1 Classical Matrix Norms;142 12.2;7.2 Indices Based on Eigenvaluesand Eigenvectors;144 12.3;7.3 Risk-Adjusted Difference Indices;146 12.3.1;7.3.1 The Direction of the Transition (DIR);146 12.
3.2;7.3.2 Transition to a Default or Nondefault State (TD);147 12.3.3;7.3.3 The Probability Mass of the Cell (PM);148 12.3.4;7.3.4 Migration Distance (MD);149 12.3.5;7.3.5 Devising a Distance Measure;149 12.3.6;7.3.6 Difference Indices for the Exemplary Matrices;153 12.4;7.4 Summary;155 13;Chapter 8. Real-World and Risk-Neutral Transition Matrices;158 13.1;8.1 The JLT Model;158 13.2;8.2 Adjustments Based on the Discrete-Time Transition Matrix;161 13.3;8.3 Adjustments Based on the Generator Matrix;164 13.3.1;8.3.1 Modifying Default Intensities;165 13.3.2;8.3.2 Modifying the Rows of the Generator Matrix;166 13.3.3;8.3.3 Modifying Eigenvalues of the TransitionProbability Matrix;167 13.4;8.4 An Adjustment Technique Basedon Economic Theory;169 13.5;8.5 Risk-Neutral Migration Matrices and Pricing;170 14;Chapter 9. Conditional Credit Migrations: Adjustments and Forecasts;172 14.1;9.1 Overview;172 14.2;9.2 The CreditPortfolioView Approach;173 14.3;9.3 Adjustment Based on Factor Model Representations;178 14.3.1;9.3.1 Deriving an Index for the Credit Cycle;179 14.3.2;9.3.2 Conditioning of the Migration Matrix;180 14.3.3;9.3.3 A Multifactor Model Extension;184 14.4;9.4 Other Methods;186 14.5;9.5 An Empirical Study on Different Forecasting Methods;188 14.5.1;9.5.1 Forecasts Using the Factor Model Approach;189 14.5.2;9.5.2 Forecasts Using Numerical Adjustment Methods;191 14.5.3;9.5.3 Regression Models;192 14.5.4;9.5.4 In-Sample Results;193 14.5.5;9.5.5 Out-of-Sample Forecasts;197 15;Chapter 10. Dependence Modeling and Credit Migrations;200 15.1;10.1 Introduction;200 15.1.1;10.1.1 Independence;201 15.1.2;10.1.2 Dependence;202 15.2;10.2 Capturing the Structure of Dependence;204 15.2.1;10.2.1 Under General Multivariate Distributions;208 15.3;10.3 Copulas;209 15.3.1;10.3.1 Examples of Copulas;211 15.3.2;10.3.2 Properties of Copulas;212 15.3.3;10.3.3 Constructing Multivariate Distributions with Copulas;213 15.4;10.4 Modeling Dependent Defaults;214 15.5;10.5 Modeling Dependent Migrati
ons;217 15.5.1;10.5.1 Dependence Based on a Credit Cycle Index;218 15.5.2;10.5.2 Dependence Based on Individual Transitions;219 15.5.3;10.5.3 Approaches Using Copulas;220 15.6;10.6 An Empirical Study on Dependent Migrations;222 15.6.1;10.6.1 Distribution of Defaults;222 15.6.2;10.6.2 The Distribution of Rating Changes;225 16;Chapter 11. Credit Derivatives;230 16.1;11.1 Introduction;230 16.1.1;11.1.1 Types of Credit Derivatives;232 16.1.2;11.1.2 Collateralized Debt Obligations (CDO);235 16.2;11.2 Pricing Single-Named Credit Derivatives;237 16.3;11.3 Modeling and Pricing of Collateralized Debt Obligations and Basket Credit Derivatives;244 16.3.1;11.3.1 Estimation of Macroeconomic Risk Factors;248 16.3.2;11.3.2 Modeling of Conditional Migrations and Recovery Rates;250 16.3.3;11.3.3 Some Empirical Results;251 16.4;11.4 Pricing Step-Up Bonds;256 16.4.1;11.4.1 Step-Up Bonds;257 16.4.2;11.4.2 Pricing of Step-Up Bonds;257 17;Bibliography;262 18;Index;272
