Rating Based Modeling of Credit Risk
Theory and Application of Migration Matrices
By: Stefan Trueck, Zari Rachev
Hardcover | 8 December 2008
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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.
*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,
Industry Reviews
Preface | p. xi |
Introduction: Credit Risk Modeling, Ratings, and Migration Matrices | p. 1 |
Motivation | p. 1 |
Structural and Reduced Form Models | p. 2 |
Basel II, Scoring Techniques, and Internal Rating Systems | p. 3 |
Rating Based Modeling and the Pricing of Bonds | p. 4 |
Stability of Transition Matrices, Conditional Migrations and Dependence | p. 5 |
Credit Derivative Pricing | p. 6 |
Chapter Outline | p. 7 |
Rating and Scoring Techniques | p. 11 |
Rating Agencies, Rating Processes, and Factors | p. 11 |
The Rating Process | p. 14 |
Credit Rating Factors | p. 16 |
Types of Rating Systems | p. 17 |
Scoring Systems | p. 17 |
Discriminant Analysis | p. 19 |
Logit and Probit Models | p. 21 |
Logit Models | p. 22 |
Probit Models | p. 23 |
Model Evaluation: Methods and Difficulties | p. 25 |
Model Performance and Benchmarking | p. 25 |
Model Accuracy, Type I and II Errors | p. 29 |
The New Basel Capital Accord | p. 31 |
Overview | p. 31 |
The First Pillar-Minimum Capital Requirement | p. 33 |
The Second Pillar-Supervisory Review Process | p. 35 |
The Third Pillar-Market Discipline | p. 35 |
The Standardized Approach | p. 36 |
Risk Weights for Sovereigns and for Banks | p. 36 |
Risk Weights for Corporates | p. 39 |
Maturity | p. 39 |
Credit Risk Mitigation | p. 40 |
The Internal Ratings Based Approach | p. 41 |
Key Elements and Risk Components | p. 41 |
Derivation of the Benchmark Risk Weight Function | p. 42 |
Asset Correlation | p. 46 |
The Maturity Adjustment | p. 48 |
Expected, Unexpected Losses and the Required Capital | p. 50 |
Summary | p. 50 |
Rating Based Modeling | p. 53 |
Introduction | p. 53 |
Reduced Form and Intensity Models | p. 54 |
The Model by Jarrow and Turnbull (1995) | p. 59 |
The Model Suggested by Madan and Unal (1998) | p. 60 |
The Model Suggested by Lando (1998) | p. 61 |
The Model of Duffie and Singleton (1999) | p. 63 |
The CreditMetrics Model | p. 63 |
The CreditRisk[superscript +] Model | p. 68 |
The First Modeling Approach | p. 68 |
Modeling Severities | p. 69 |
Shortcomings of the First Modeling Approach | p. 71 |
Extensions in the CR[superscript +] Model | p. 72 |
Allocating Obligors to One of Several Factors | p. 72 |
The pgf for the Number of Defaults | p. 73 |
The pgf for the Default Loss Distribution | p. 75 |
Generalization of Obligor Allocation | p. 75 |
The Default Loss Distribution | p. 76 |
Migration Matrices and the Markov Chain Approach | p. 77 |
The Markov Chain Approach | p. 77 |
Generator Matrices | p. 78 |
Discrete Versus Continuous-Time Modeling | p. 80 |
Some Conditions for the Existence of a Valid Generator | p. 86 |
Approximation of Generator Matrices | p. 88 |
The Method Proposed by Jarrow, Lando, and Turnbull (1997) | p. 88 |
Methods Suggested by Israel, Rosenthal, and Wei (2000) | p. 89 |
Simulating Credit Migrations | p. 92 |
Time-Discrete Case | p. 92 |
Time-Continuous Case | p. 93 |
Nonparametric Approach | p. 94 |
Stability of Credit Migrations | p. 97 |
Credit Migrations and the Business Cycle | p. 97 |
The Markov Assumptions and Rating Drifts | p. 102 |
Likelihood Ratio Tests | p. 103 |
Rating Drift | p. 104 |
An Empirical Study | p. 105 |
Time Homogeneity of Migration Matrices | p. 109 |
Tests Using the Chi-Square Distance | p. 110 |
Eigenvalues and Eigenvectors | p. 110 |
Migration Behavior and Effects on Credit VaR | p. 113 |
Stability of Probability of Default Estimates | p. 120 |
Measures for Comparison of Transition Matrices | p. 129 |
Classical Matrix Norms | p. 129 |
Indices Based on Eigenvalues and Eigenvectors | p. 131 |
Risk-Adjusted Difference Indices | p. 133 |
The Direction of the Transition (DIR) | p. 133 |
Transition to a Default or Nondefault State (TD) | p. 134 |
The Probability Mass of the Cell (PM) | p. 135 |
Migration Distance (MD) | p. 136 |
Devising a Distance Measure | p. 136 |
Difference Indices for the Exemplary Matrices | p. 140 |
Summary | p. 142 |
Real-World and Risk-Neutral Transition Matrices | p. 145 |
The JLT Model | p. 145 |
Adjustments Based on the Discrete-Time Transition Matrix | p. 148 |
Adjustments Based on the Generator Matrix | p. 151 |
Modifying Default Intensities | p. 152 |
Modifying the Rows of the Generator Matrix | p. 153 |
Modifying Eigenvalues of the Transition Probability Matrix | p. 154 |
An Adjustment Technique Based on Economic Theory | p. 156 |
Risk-Neutral Migration Matrices and Pricing | p. 157 |
Conditional Credit Migrations: Adjustments and Forecasts | p. 159 |
Overview | p. 159 |
The CreditPortfolioView Approach | p. 160 |
Adjustment Based on Factor Model Representations | p. 165 |
Deriving an Index for the Credit Cycle | p. 166 |
Conditioning of the Migration Matrix | p. 167 |
A Multifactor Model Extension | p. 171 |
Other Methods | p. 173 |
An Empirical Study on Different Forecasting Methods | p. 175 |
Forecasts Using the Factor Model Approach | p. 176 |
Forecasts Using Numerical Adjustment Methods | p. 178 |
Regression Models | p. 179 |
In-Sample Results | p. 180 |
Out-of-Sample Forecasts | p. 184 |
Dependence Modeling and Credit Migrations | p. 187 |
Introduction | p. 187 |
Independence | p. 188 |
Dependence | p. 189 |
Capturing the Structure of Dependence | p. 191 |
Under General Multivariate Distributions | p. 195 |
Copulas | p. 196 |
Examples of Copulas | p. 198 |
Properties of Copulas | p. 199 |
Constructing Multivariate Distributions with Copulas | p. 200 |
Modeling Dependent Defaults | p. 201 |
Modeling Dependent Migrations | p. 204 |
Dependence Based on a Credit Cycle Index | p. 205 |
Dependence Based on Individual Transitions | p. 206 |
Approaches Using Copulas | p. 207 |
An Empirical Study on Dependent Migrations | p. 209 |
Distribution of Defaults | p. 209 |
The Distribution of Rating Changes | p. 212 |
Credit Derivatives | p. 217 |
Introduction | p. 217 |
Types of Credit Derivatives | p. 219 |
Collateralized Debt Obligations (CDO) | p. 222 |
Pricing Single-Named Credit Derivatives | p. 224 |
Modeling and Pricing of Collateralized Debt Obligations and Basket Credit Derivatives | p. 231 |
Estimation of Macroeconomic Risk Factors | p. 235 |
Modeling of Conditional Migrations and Recovery Rates | p. 237 |
Some Empirical Results | p. 238 |
Pricing Step-Up Bonds | p. 243 |
Step-Up Bonds | p. 244 |
Pricing of Step-Up Bonds | p. 244 |
Bibliography | p. 249 |
Index | p. 259 |
Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780123736833
ISBN-10: 0123736838
Series: Academic Press Advanced Finance
Published: 8th December 2008
Format: Hardcover
Language: English
Number of Pages: 280
Audience: Professional and Scholarly
Publisher: Academic Press
Country of Publication: US
Dimensions (cm): 22.9 x 15.2 x 2.54
Weight (kg): 0.58
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