Concentration Risk in Credit Portfolios

Transcription

1 Eva Liitkebohmert Concentration Risk in Credit Portfolios With 17 Figures and 19 Tables 4y Springer

2 Contents Part I Introduction to Credit Risk Modeling 1 Risk Measurement Variables of Risk The General Model Setting Exchangeable Models 7 2 Modeling Credit Risk The Regulatory Framework Expected and Unexpected Loss Value-at-Risk Expected Shortfall Economic Capital 17 3 The Merton Model The General Framework The Multi-Factor Merton Model Industry Models Based on the Merton Approach The KMV Model The CreditMetrics Model 30 4 The Asymptotic Single Risk Factor Model The ASRF Model The IRB Risk Weight Functions The Loss Distribution of an Infinitely Granular Portfolio 38 5 Mixture Models Bernoulli and Poisson Mixture Models The Influence of the Mixing Distribution on the Loss Distribution Relation Between Latent Variable Models and Mixture Models 50

3 X Contents 6 The CreditRisk+ Model Basic Model Setting The Poisson Approximation Model with Random Default Probabilities 57 Part II Concentration Risk in Credit Portfolios 7 Introduction 63 8 Ad-Hoc Measures of Concentration Concentration Indices Conclusion 72 9 Name Concentration A Granularity Adjustment for the ASRF Model Example as Motivation for GA Methodology The General Framework The Granularity Adjustment in a Single Factor CreditRisk+ Setting Data on German Bank Portfolios Numerical Results Summary The Semi-Asymptotic Approach The General Framework Numerical Results Methods Based on the Saddle-Point Approximation The General Framework Application to Name Concentration Risk Discussion and Comparison Study of the Granularity Adjustment Methods Empirical Relevance of the Granularity Adjustment Why a Granularity Adjustment Instead of the HHI? Accuracy of the Granularity Adjustment and Robustness to Regulatory Parameters Comparison of Granularity Adjustment with Other Model-Based Approaches Agreement of Granularity Adjustment and Saddle- Point Approximation Method in the CreditRisk" 1 " Model Sector Concentration Analytical Approximation Models. ' Analytical Approximation for Value-at-Risk Analytical Approximation for Expected Shortfall Performance Testing 118

4 Contents XI Summary and Discussion Diversification Factor Models The Multi-Sector Framework The Capital Diversification Factor Marginal Capital Contributions Parameterization Application to a Bank Internal Multi-Factor Model Discussion Empirical Studies on Concentration Risk Sector Concentration and Economic Capital The Model Framework Data Description and Portfolio Composition Impact of Sector Concentration on Economic Capital Robustness of EC Approximations Discussion The Influence of Systematic and Idiosyncratic Risk on Large Portfolio Losses Descriptive Analysis of SNC Data Simple Indices of Name and Sector Concentration Modeling Dependencies in Losses Monte Carlo Simulation of the Portfolio Loss Distribution Empirical Results Summary and Discussion 147 Part III Default Contagion 12 Introduction Empirical Studies on Default Contagion The Doubly Stochastic Property and its Testable Implications Data for Default Intensity Estimates Goodness-of-Fit Tests Discussion Models Based on Copulas Equivalence of Latent Variable Models Sensitivity of Losses on the Dependence Structure Discussion 170

5 XII Contents 15 A Voter Model for Credit Contagion The Model Framework Invariant and Ergodic Measures for the Voter Model The Non-Dense Business Partner Network The Dense Business Partner Network Aggregate Losses on Large Portfolios Discussion and Comparison with Alternative Approaches The Mean-Field Model with Interacting Default Intensities A Dynamic Contagion Model Contagion Through Macro- and Microstructural Channels A Model with Macro- and Micro-Structural Dependence The Rating Migrations Process Results and Discussion Equilibrium Models A Mean-Field Model of Credit Ratings The Mean-Field Model with Local Interactions Large Portfolio Losses Discussion 208 A Copulas 211 References 217 Index 223