Rating Based Modeling of Credit Risk Theory and Application of Migration Matrices

Transcription

1 Rating Based Modeling of Credit Risk Theory and Application of Migration Matrices

2 Preface xi 1 Introduction: Credit Risk Modeling, Ratings, and Migration Matrices Motivation Structural and Reduced Form Models Basel II, Scoring Techniques, and Internal Rating Systems Rating Based Modeling and the Pricing of Bonds Stability of Transition Matrices, Conditional Migrations and Dependence Credit Derivative Pricing Chapter Outline 7 2 Rating and Scoring Techniques Rating Agencies, Rating Processes, and Factors The Rating Process Credit Rating Factors Types of Rating Systems Scoring Systems Discriminant Analysis Logit and Probit Models Logit Models Probit Models Model Evaluation: Methods and Difficulties Model Performance and Benchmarking Model Accuracy, Type I and II Errors 29 3 The New Basel Capital Accord Overview The First Pillar Minimum Capital Requirement The Second Pillar Supervisory Review Process The Third Pillar Market Discipline The Standardized Approach Risk Weights for Sovereigns and for Banks Risk Weights for Corporates Maturity Credit Risk Mitigation The Internal Ratings Based Approach Key Elements and Risk Components Derivation of the Benchmark Risk Weight Function Asset Correlation The Maturity Adjustment Expected, Unexpected Losses and the Required Capital Summary 50

3 Rating Based Modeling Introduction Reduced Form and Intensity Models The Model by Jarrow and Turnbull (1995) The Model Suggested by Madan and Unal (1998) The Model Suggested by Lando (1998) The Model of Duffie and Singleton (1999) The CreditMetrics Model The CreditRisk+ Model The First Modeling Approach Modeling Severities Shortcomings of the First Modeling Approach Extensions in the CR+ Model Allocating Obligors to One of Several Factors The pgf for the Number of Defaults The pgf for the Default Loss Distribution Generalization of Obligor Allocation The Default Loss Distribution 76 Migration Matrices and the Markov Chain Approach The Markov Chain Approach Generator Matrices Discrete Versus Continuous-Time Modeling Some Conditions for the Existence of a Valid Generator Approximation of Generator Matrices The Method Proposed by Jarrow, Lando, and Turnbull (1997) Methods Suggested by Israel, Rosenthal, and Wei (2000) Simulating Credit Migrations Time-Discrete Case Time-Continuous Case Nonparametric Approach 94 Stability of Credit Migrations Credit Migrations and the Business Cycle The Markov Assumptions and Rating Drifts Likelihood Ratio Tests Rating Drift An Empirical Study Time Homogeneity of Migration Matrices Tests Using the Chi-Square Distance Eigenvalues and Eigenvectors Migration Behavior and Effects on Credit VaR Stability of Probability of Default Estimates 120 Measures for Comparison of Transition Matrices Classical Matrix Norms Indices Based on Eigenvalues and Eigenvectors Risk-Adjusted Difference Indices The Direction of the Transition (DIR) Transition to a Default or Nondefault State (TD) The Probability Mass of the Cell (PM) 135

4 ix Migration Distance (MD) Devising a Distance Measure Difference Indices for the Exemplary Matrices Summary Real-World and Risk-Neutral Transition Matrices The JLT Model Adjustments Based on the Discrete-Time Transition Matrix Adjustments Based on the Generator Matrix Modifying Default Intensities Modifying the Rows of the Generator Matrix Modifying Eigenvalues of the Transition Probability Matrix An Adjustment Technique Based on Economic Theory Risk-Neutral Migration Matrices and Pricing Conditional Credit Migrations: Adjustments and Forecasts Overview The CreditPortfolioView Approach Adjustment Based on Factor Model Representations Deriving an Index for the Credit Cycle Conditioning of the Migration Matrix A Multifactor Model Extension Other Methods An Empirical Study on Different Forecasting Methods Forecasts Using the Factor Model Approach Forecasts Using Numerical Adjustment Methods Regression Models In-Sample Results Out-of-Sample Forecasts Dependence Modeling and Credit Migrations Introduction Independence Dependence Capturing the Structure of Dependence Under General Multivariate Distributions Copulas Examples of Copulas Properties of Copulas Constructing Multivariate Distributions with Copulas Modeling Dependent Defaults Modeling Dependent Migrations Dependence Based on a Credit Cycle Index Dependence Based on Individual Transitions Approaches Using Copulas An Empirical Study on Dependent Migrations Distribution of Defaults The Distribution of Rating Changes Credit Derivatives Introduction Types of Credit Derivatives Collateralized Debt Obligations (CDO) 222

5 x Contents 11.2 Pricing Single-Named Credit Derivatives Modeling and Pricing of Collateralized Debt Obligations and Basket Credit Derivatives Estimation of Macroeconomic Risk Factors Modeling of Conditional Migrations and Recovery Rates Some Empirical Results Pricing Step-Up Bonds Step-Up Bonds Pricing of Step-Up Bonds 244 Bibliography 249 Index 259