Levy Processes in Credit Risk

Abstract

Preface. Acknowledgements. PART I: INTRODUCTION. 1 An Introduction to Credit Risk. 1.1 Credit Risk. 1.1.1 Historical and Risk-Neutral Probabilities. 1.1.2 Bond Prices and Default Probability. 1.2 Credit Risk Modelling. 1.3 Credit Derivatives. 1.4 Modelling Assumptions. 1.4.1 Probability Space and Filtrations. 1.4.2 The Risk-Free Asset. 2 An Introduction to Levy Processes. 2.1 Brownian Motion. 2.2 Levy Processes. 2.3 Examples of Levy Processes. 2.3.1 Poisson Process. 2.3.2 Compound Poisson Process. 2.3.3 The Gamma Process. 2.3.4 Inverse Gaussian Process. 2.3.5 The CMY Process. 2.3.6 The Variance Gamma Process. 2.4 Ornstein-Uhlenbeck Processes. 2.4.1 The Gamma-OU Process. 2.4.2 The Inverse Gaussian-OU Process. PART II: SINGLE-NAME MODELLING. 3 Single-Name Credit Derivatives. 3.1 Credit Default Swaps. 3.1.1 Credit Default Swaps Pricing. 3.1.2 Calibration Assumptions. 3.2 Credit Default Swap Forwards. 3.2.1 Credit Default Swap Forward Pricing. 3.3 Constant Maturity Credit Default Swaps. 3.3.1 Constant Maturity Credit Default Swaps Pricing. 3.4 Options on CDS. 4 Firm-Value Levy Models. 4.1 The Merton Model. 4.2 The Black-Cox Model with Constant Barrier. 4.3 The Levy First-Passage Model. 4.4 The Variance Gamma Model. 4.4.1 Sensitivity to the Parameters. 4.4.2 Calibration on CDS Term Structure Curve. 4.5 One-Sided Levy Default Model. 4.5.1 Wiener-Hopf Factorization and Default Probabilities. 4.5.2 Illustration of the Pricing of Credit Default Swaps. 4.6 Dynamic Spread Generator. 4.6.1 Generating Spread Paths. 4.6.2 Pricing of Options on CDSs. 4.6.3 Black's Formulas and Implied Volatility. Appendix: Solution of the PDIE. 5 IntensityLevy Models. 5.1 Intensity Models for Credit Risk. 5.1.1 Jarrow-Turnbull Model. 5.1.2 Cox Models. 5.2 The Intensity-OU Model. 5.3 Calibration of the Model on CDS Term Structures. PART III: MULTIVARIATE MODELLING. 6 Multivariate Credit Products. 6.1 CDOs. 6.2 Credit Indices. 7 Collateralized Debt Obligations. 7.1 Introduction. 7.2 The Gaussian One-Factor Model. 7.3 Generic One-Factor Levy Model. 7.4 Examples of Levy Models. 7.5 Levy Base Correlation. 7.5.1 The Concept of Base Correlation. 7.5.2 Pricing Non-Standard Tranches. 7.5.3 Correlation Mapping for Bespoke CDOs. 7.6 Delta-Hedging CDO tranches. 7.6.1 Hedging with the CDS Index. 7.6.2 Delta-Hedging with a Single-Name CDS. 7.6.3 Mezz-Equity hedging. 8 Multivariate Index Modelling. 8.1 Black's Model. 8.2 VG Credit Spread Model. 8.3 Pricing Swaptions using FFT. 8.4 Multivariate VG Model. PART IV: EXOTIC STRUCTURED CREDIT RISK PRODUCTS. 9 Credit CPPIs and CPDOs. 9.1 Introduction. 9.2 CPPIs. 9.3 Gap Risk. 9.4 CPDOs. 10 Asset-Backed Securities. 10.1 Introduction. 10.2 Default Models. 10.2.1 Generalized Logistic Default Model. 10.2.2 Levy Portfolio Default Model. 10.2.3 Normal One-Factor Default Model. 10.2.4 Generic One-Factor Levy Default Model. 10.3 Prepayment Models. 10.3.1 Constant Prepayment Model. 10.3.2 Levy Portfolio Prepayment Model. 10.3.3 Normal One-Factor Prepayment Model. 10.4 Numerical Results. Bibliography. Index.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 68 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.