| Introduction to Credit Risk Modeling | |
| Risk Measurement | p. 3 |
| Variables of Risk | p. 4 |
| The General Model Setting | p. 5 |
| Exchangeable Models | p. 7 |
| Modeling Credit Risk | p. 9 |
| The Regulatory Framework | p. 10 |
| Expected and Unexpected Loss | p. 12 |
| Value-at-Risk | p. 13 |
| Expected Shortfall | p. 15 |
| Economic Capital | p. 17 |
| The Merton Model | p. 19 |
| The General Framework | p. 20 |
| The Multi-Factor Merton Model | p. 23 |
| Industry Models Based on the Merton Approach | p. 29 |
| The KMV Model | p. 29 |
| The CreditMetrics Model | p. 30 |
| The Asymptotic Single Risk Factor Model | p. 31 |
| The ASRF Model | p. 32 |
| The IRB Risk Weight Functions | p. 35 |
| The Loss Distribution of an Infinitely Granular Portfolio | p. 38 |
| Mixture Models | p. 43 |
| Bernoulli and Poisson Mixture Models | p. 43 |
| The Influence of the Mixing Distribution on the Loss Distribution | p. 48 |
| Relation Between Latent Variable Models and Mixture Models | p. 50 |
| The CreditRisk[superscript +] Model | p. 53 |
| Basic Model Setting | p. 54 |
| The Poisson Approximation | p. 56 |
| Model with Random Default Probabilities | p. 57 |
| Concentration Risk in Credit Portfolios | |
| Introduction | p. 63 |
| Ad-Hoc Measures of Concentration | p. 67 |
| Concentration Indices | p. 68 |
| Conclusion | p. 72 |
| Name Concentration | p. 75 |
| A Granularity Adjustment for the ASRF Model | p. 76 |
| Example as Motivation for GA Methodology | p. 77 |
| The General Framework | p. 78 |
| The Granularity Adjustment in a Single Factor CreditRisk[superscript +] Setting | p. 81 |
| Data on German Bank Portfolios | p. 84 |
| Numerical Results | p. 86 |
| Summary | p. 88 |
| The Semi-Asymptotic Approach | p. 90 |
| The General Framework | p. 90 |
| Numerical Results | p. 93 |
| Methods Based on the Saddle-Point Approximation | p. 93 |
| The General Framework | p. 94 |
| Application to Name Concentration Risk | p. 96 |
| Discussion and Comparison Study of the Granularity Adjustment Methods | p. 99 |
| Empirical Relevance of the Granularity Adjustment | p. 100 |
| Why a Granularity Adjustment Instead of the HHI? | p. 100 |
| Accuracy of the Granularity Adjustment and Robustness to Regulatory Parameters | p. 102 |
| Comparison of Granularity Adjustment with Other Model-Based Approaches | p. 103 |
| Agreement of Granularity Adjustment and Saddle-Point Approximation Method in the CreditRisk[superscript +] Model | p. 104 |
| Sector Concentration | p. 107 |
| Analytical Approximation Models | p. 108 |
| Analytical Approximation for Value-at-Risk | p. 109 |
| Analytical Approximation for Expected Shortfall | p. 117 |
| Performance Testing | p. 118 |
| Summary and Discussion | p. 119 |
| Diversification Factor Models | p. 120 |
| The Multi-Sector Framework | p. 121 |
| The Capital Diversification Factor | p. 123 |
| Marginal Capital Contributions | p. 124 |
| Parameterization | p. 126 |
| Application to a Bank Internal Multi-Factor Model | p. 127 |
| Discussion | p. 129 |
| Empirical Studies on Concentration Risk | p. 131 |
| Sector Concentration and Economic Capital | p. 132 |
| The Model Framework | p. 133 |
| Data Description and Portfolio Composition | p. 133 |
| Impact of Sector Concentration on Economic Capital | p. 135 |
| Robustness of EC Approximations | p. 136 |
| Discussion | p. 139 |
| The Influence of Systematic and Idiosyncratic Risk on Large Portfolio Losses | p. 140 |
| Descriptive Analysis of SNC Data | p. 140 |
| Simple Indices of Name and Sector Concentration | p. 141 |
| Modeling Dependencies in Losses | p. 142 |
| Monte Carlo Simulation of the Portfolio Loss Distribution | p. 143 |
| Empirical Results | p. 145 |
| Summary and Discussion | p. 147 |
| Default Contagion | |
| Introduction | p. 151 |
| Empirical Studies on Default Contagion | p. 155 |
| The Doubly Stochastic Property and its Testable Implications | p. 156 |
| Data for Default Intensity Estimates | p. 159 |
| Goodness-of-Fit Tests | p. 159 |
| Discussion | p. 162 |
| Models Based on Copulas | p. 165 |
| Equivalence of Latent Variable Models | p. 166 |
| Sensitivity of Losses on the Dependence Structure | p. 168 |
| Discussion | p. 170 |
| A Voter Model for Credit Contagion | p. 173 |
| The Model Framework | p. 174 |
| Invariant and Ergodic Measures for the Voter Model | p. 177 |
| The Non-Dense Business Partner Network | p. 179 |
| The Dense Business Partner Network | p. 180 |
| Aggregate Losses on Large Portfolios | p. 182 |
| Discussion and Comparison with Alternative Approaches | p. 186 |
| The Mean-Field Model with Interacting Default Intensities | p. 187 |
| A Dynamic Contagion Model | p. 189 |
| Contagion Through Macro- and Microstructural Channels | p. 190 |
| A Model with Macro- and Micro-Structural Dependence | p. 191 |
| The Rating Migrations Process | p. 193 |
| Results and Discussion | p. 194 |
| Equilibrium Models | p. 197 |
| A Mean-Field Model of Credit Ratings | p. 198 |
| The Mean-Field Model with Local Interactions | p. 202 |
| Large Portfolio Losses | p. 205 |
| Discussion | p. 208 |
| A Copulas | p. 211 |
| References | p. 217 |
| Index | p. 223 |
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