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Table of Contents
Intro; Foreword; Preface; My Motivation; Transparency and Accessibility; Concreteness; Multiplicity of Perspective; Some Important Caveats; References; Acknowledgements; Contents; List of Figures; List of Tables; List of Algorithms; 1 Getting Started; 1.1 Alternative Perspectives; 1.1.1 Pricing or Risk-Management?; 1.1.2 Minding our P's and Q's; 1.1.3 Instruments or Portfolios?; 1.1.4 The Time Dimension; 1.1.5 Type of Credit-Risk Model; 1.1.6 Clarifying Our Perspective; 1.2 A Useful Dichotomy; 1.2.1 Modelling Implications; 1.2.2 Rare Events; 1.3 Seeing the Forest; 1.3.1 Modelling Frameworks
1.3.2 Diagnostic Tools1.3.3 Estimation Techniques; 1.3.4 The Punchline; 1.4 Prerequisites; 1.5 Our Sample Portfolio; 1.6 A Quick Pre-Screening; 1.6.1 A Closer Look at Our Portfolio; 1.6.2 The Default-Loss Distribution; 1.6.3 Tail Probabilities and Risk Measures; 1.6.4 Decomposing Risk; 1.6.5 Summing Up; 1.7 Final Thoughts; References; Part I Modelling Frameworks; Reference; 2 A Natural First Step; 2.1 Motivating a Default Model; A Bit of Structure; 2.1.1 Two Instruments; 2.1.2 Multiple Instruments; 2.1.3 Dependence; 2.2 Adding Formality; 2.2.1 An Important Aside; 2.2.2 A Numerical Solution
2.2.2.1 Bernoulli Trials2.2.2.2 Practical Details; 2.2.2.3 Some Results; 2.2.3 An Analytical Approach; 2.2.3.1 Putting It into Action; 2.2.3.2 Comparing Key Assumptions; 2.3 Convergence Properties; Convergence in Probability; Almost-Sure Convergence; Cutting to the Chase; 2.4 Another Entry Point; A Numerical Implementation; The Analytic Model; The Law of Rare Events; 2.5 Final Thoughts; References; 3 Mixture or Actuarial Models; 3.1 Binomial-Mixture Models; Conditional Independence; Default-Correlation Coefficient; The Distribution of DN; Convergence Properties
3.1.1 The Beta-Binomial Mixture Model3.1.1.1 Beta-Parameter Calibration; 3.1.1.2 Back to Our Example; 3.1.1.3 Non-homogeneous Exposures; 3.1.2 The Logit- and Probit-Normal Mixture Models; 3.1.2.1 Deriving the Mixture Distributions; 3.1.2.2 Numerical Integration; 3.1.2.3 Logit- and Probit-Normal Calibration; 3.1.2.4 Logit- and Probit-Normal Results; 3.2 Poisson-Mixture Models; 3.2.1 The Poisson-Gamma Approach; 3.2.1.1 Calibrating the Poisson-Gamma Mixture Model; 3.2.1.2 A Quick and Dirty Calibration; 3.2.1.3 Poisson-Gamma Results; 3.2.2 Other Poisson-Mixture Approaches
3.2.2.1 A Calibration Comparison3.2.3 Poisson-Mixture Comparison; 3.3 CreditRisk+; 3.3.1 A One-Factor Implementation; 3.3.2 A Multi-Factor CreditRisk+ Example; 3.4 Final Thoughts; References; 4 Threshold Models; 4.1 The Gaussian Model; 4.1.1 The Latent Variable; 4.1.2 Introducing Dependence; 4.1.3 The Default Trigger; 4.1.4 Conditionality; 4.1.5 Default Correlation; 4.1.6 Calibration; 4.1.7 Gaussian Model Results; 4.2 The Limit-Loss Distribution; 4.2.1 The Limit-Loss Density; 4.2.2 Analytic Gaussian Results; 4.3 Tail Dependence; 4.3.1 The Tail-Dependence Coefficient
1.3.2 Diagnostic Tools1.3.3 Estimation Techniques; 1.3.4 The Punchline; 1.4 Prerequisites; 1.5 Our Sample Portfolio; 1.6 A Quick Pre-Screening; 1.6.1 A Closer Look at Our Portfolio; 1.6.2 The Default-Loss Distribution; 1.6.3 Tail Probabilities and Risk Measures; 1.6.4 Decomposing Risk; 1.6.5 Summing Up; 1.7 Final Thoughts; References; Part I Modelling Frameworks; Reference; 2 A Natural First Step; 2.1 Motivating a Default Model; A Bit of Structure; 2.1.1 Two Instruments; 2.1.2 Multiple Instruments; 2.1.3 Dependence; 2.2 Adding Formality; 2.2.1 An Important Aside; 2.2.2 A Numerical Solution
2.2.2.1 Bernoulli Trials2.2.2.2 Practical Details; 2.2.2.3 Some Results; 2.2.3 An Analytical Approach; 2.2.3.1 Putting It into Action; 2.2.3.2 Comparing Key Assumptions; 2.3 Convergence Properties; Convergence in Probability; Almost-Sure Convergence; Cutting to the Chase; 2.4 Another Entry Point; A Numerical Implementation; The Analytic Model; The Law of Rare Events; 2.5 Final Thoughts; References; 3 Mixture or Actuarial Models; 3.1 Binomial-Mixture Models; Conditional Independence; Default-Correlation Coefficient; The Distribution of DN; Convergence Properties
3.1.1 The Beta-Binomial Mixture Model3.1.1.1 Beta-Parameter Calibration; 3.1.1.2 Back to Our Example; 3.1.1.3 Non-homogeneous Exposures; 3.1.2 The Logit- and Probit-Normal Mixture Models; 3.1.2.1 Deriving the Mixture Distributions; 3.1.2.2 Numerical Integration; 3.1.2.3 Logit- and Probit-Normal Calibration; 3.1.2.4 Logit- and Probit-Normal Results; 3.2 Poisson-Mixture Models; 3.2.1 The Poisson-Gamma Approach; 3.2.1.1 Calibrating the Poisson-Gamma Mixture Model; 3.2.1.2 A Quick and Dirty Calibration; 3.2.1.3 Poisson-Gamma Results; 3.2.2 Other Poisson-Mixture Approaches
3.2.2.1 A Calibration Comparison3.2.3 Poisson-Mixture Comparison; 3.3 CreditRisk+; 3.3.1 A One-Factor Implementation; 3.3.2 A Multi-Factor CreditRisk+ Example; 3.4 Final Thoughts; References; 4 Threshold Models; 4.1 The Gaussian Model; 4.1.1 The Latent Variable; 4.1.2 Introducing Dependence; 4.1.3 The Default Trigger; 4.1.4 Conditionality; 4.1.5 Default Correlation; 4.1.6 Calibration; 4.1.7 Gaussian Model Results; 4.2 The Limit-Loss Distribution; 4.2.1 The Limit-Loss Density; 4.2.2 Analytic Gaussian Results; 4.3 Tail Dependence; 4.3.1 The Tail-Dependence Coefficient