Rating Based Modeling of Credit Risk

Theory and Application of Migration Matrices


  • Stefan Trueck, Postdoctoral Research Fellow, School of Economics and Finance, Queensland University of Technology, Australia
  • Svetlozar Rachev, Chair-Professor at the University of Karlsruhe in the School of Economics and Business Engineering

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 this book 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.
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Primary readership: Both researchers, practitioners and financial institutions in the area of banking, mathematical finance, risk management, especially credit risk management.Secondary readership: The book may also be used as textbook in an advanced course on credit risk or credit risk modelling..


Book information

  • Published: December 2008
  • ISBN: 978-0-12-373683-3


"... an excellent overview of theory and application...." -Frank J. Fabozzi, PhD, CFA, Professor in the Practice of Finance, Yale School of Management, CT

Table of Contents

1 Introduction: Credit Risk Modeling, Ratings and Migration Matrices 1.1 Motivation1.2 StructuralandReducedFormModels 1.3 Basel II, Scoring Techniques and Internal Rating Systems 1.4 Rating Based Modeling and the Pricing of Bonds 1.5 Stability of Transition Matrices, Conditional Migrations and Dependence 1.6 CreditDerivativePricing 1.7 ChapterOutline2 Rating and Scoring Techniques 2.1 Ratings Agencies, Rating Processes and Factors2.2 ScoringSystems2.3 Discriminantanalysis2.4 LogitandProbitModels2.5 Model Evaluation: Methods and Difficulties 3 The new Basel Capital Accord 3.1 Overview 3.2 TheStandardizedApproach3.3 TheInternalRatingsBasedApproach 3.4 Summary 4 Rating Based Modeling 4.1 Introduction4.2 ReducedFormandIntensityModels 4.3 TheCreditMetricsModel4.4 The CreditRisk+ Model5 Migration Matrices and the Markov Chain Approach 5.1 TheMarkovChainApproach 5.2 Discrete versus Continuous-Time Modeling 5.3 Approximation of Generator Matrices 5.4 SimulatingCreditMigrations 6 Stability of Credit Migrations 6.1 Credit Migrations and the Business Cycle 6.2 The Markov Assumptions and Rating Drifts 6.3 Time Homogeneity of Migration Matrices6.4 Migration Behavior and Effects on Credit VaR 6.5 Stability of Probability of Default Estimates 7 Measures for Comparison of Transition Matrices 7.1 ClassicalMatrixNorms7.2 Indices Based on Eigenvalues and Eigenvectors 7.3 Risk-AdjustedDifferenceIndices 7.4 Summary8 Real World and Risk-Neutral Transition Matrices8.1 TheJLTModel 8.2 Adjustments based on the Discrete-Time Transition Matrix8.3 Adjustments based on the Generator Matrix 8.4 An Adjustment Technique Based on Economic Theory 8.5 Risk-Neutral Migration Matrices and Pricing 9 Conditional Credit Migrations: Adjustments and Forecasts 9.1 Overview 9.2 TheCreditPortfolioViewApproach 9.3 Adjustment based on Factor Model Representations 9.4 OtherMethods 9.5 An Empirical Study on Different Forecasting Methods 10 Dependence Modeling and Credit Migrations 10.1 Introduction 10.2 Capturing the structure of dependence 10.3 Copulas 10.4 ModelingDependentDefaults10.5 ModelingDependentMigrations 10.6 An Empirical Study on Dependent Migrations 11 Credit Derivatives 11.1 Introduction11.2 Pricing Single-Named credit derivatives 11.3 Migration Matrices and CDO evaluation 11.4 PricingStep-UpBondsBibliography