Theory and Application of Migration Matrices To order this title, and for more information, click here
By 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
Description 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.
Audience
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..
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 Risk-AdjustedDifferenceIndices
7.4 Summary
8 Real World and Risk-Neutral Transition
Matrices
8.1 TheJLTModel
8.2 Adjustments based on the Discrete-Time Transition Matrix
8.3 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 ModelingDependentDefaults
10.5 ModelingDependentMigrations
10.6 An Empirical
Study on Dependent Migrations
11 Credit Derivatives
11.1 Introduction
11.2 Pricing Single-Named credit derivatives
11.3 Migration
Matrices and CDO evaluation
11.4 PricingStep-UpBonds
Bibliography
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