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 |
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