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.

Key Features

*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,


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..

Table of Contents

1 Introduction: Credit Risk Modeling, Ratings and Migration Matrices 1.1 Motivation 1.2 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 ChapterOutline 2 Rating and Scoring Techniques 2.1 Ratings Agencies, Rating Processes and Factors 2.2 ScoringSystems 2.3 Discriminantanalysis 2.4 LogitandProbitModels 2.5 Model Evaluation: Methods and Difficulties 3 The new Basel Capital Accord 3.1 Overview 3.2 TheStandardizedApproach 3.3 TheInternalRatingsBasedApproach 3.4 Summary 4 Rating Based Modeling 4.1 Introduction 4.2 ReducedFormandIntensityModels 4.3 TheCreditMetricsModel 4.4 The CreditRisk+ Model 5 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 Matrices 6.4 Migration Behavior and Effects on Credit VaR 6.5 Stability of Probability of Default Estimates 7 Measures for Comparison of Transition Matrices 7.1 ClassicalMatrixNorms 7.2 Indices Based on Eigenvalues and Eigenvectors 7.3 R


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Academic Press
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About the editors

Stefan Trueck

Affiliations and Expertise

Postdoctoral Research Fellow, School of Economics and Finance, Queensland University of Technology, Australia

Svetlozar Rachev

Svetlozar (Zari) Rachev completed his PhD in 1979 from Moscow State University, and his Doctor of Science degree in 1986 from the Steklov mathematical Institute in Moscow. Currently he is Chair-Professor at the University of Karlsruhe in the School of Economics and Business Engineering. He is also Professor Emeritus at the University of California Santa Barbara in the Dept of Statistics and Applied Probability. He has published six monographs and over 230 research articles. He is a Fellow of the Institute of Mathematical Statistics, Elected member of the International statistical Institute, foreign Member of the Russian Academy of Natural Science, and hols an honorary doctorate degree from St. Petersburg Technical University. He is co-founder of Bravo Risk Management Group specializing in financial risk management software. Bravo Group was recently acquired by FinAnalytics for which he currently serves as Chief-Scientist.

Affiliations and Expertise

Chair-Professor at the University of Karlsruhe in the School of Economics and Business Engineering


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