Levy Processes in Credit Risk (eBook)

Wim Schoutens (Leuven, Belgium) is a research professor in financial engineering in the Department of Mathematics at the Catholic University of Leuven, Belgium. He has extensive practical experience of model implementation and is well known for his consulting work in the banking industry. Wim is the author of Lévy Processes in Finance and co-editor of Exotic Option Pricing and Advanced Lévy Models both published by Wiley. He teaches at 7city Learning and London Financial Studies. He is Managing Editor of the International Journal of Theoretical and Applied Finance and Associate Editor of Mathematical Finance and Review of Derivatives Research. Jessica Cariboni (Ispra, Italy) has a PhD in applied statistics from the Catholic University of Leuven, Belgium. She was a junior quantitative analyst at Nextra Investment Management. She is currently a functionary of the European Commission and researcher at the European Commission DG-Joint Research Centre, Ispra, Italy. She is also co-author of the book Global Sensitivity Analysis: The Primer published by Wiley.

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 Lévy Processes.

2.1 Brownian Motion.

2.2 Lévy Processes.

2.3 Examples of Lévy 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 Lévy Models.

4.1 The Merton Model.

4.2 The Black-Cox Model with Constant Barrier.

4.3 The Lévy 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 Lévy Default Model.

4.5.1 Wiener-Hopf Factorization and DefaultProbabilities.

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 IntensityLévy 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 Lévy Model.

7.4 Examples of Lévy Models.

7.5 Lévy 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 Lévy Portfolio Default Model.

10.2.3 Normal One-Factor Default Model.

10.2.4 Generic One-Factor Lévy Default Model.

10.3 Prepayment Models.

10.3.1 Constant Prepayment Model.

10.3.2 Lévy Portfolio Prepayment Model.

10.3.3 Normal One-Factor Prepayment Model.

10.4 Numerical Results.

Bibliography.

Index.

"This text introduces into the use of Levy processes in credit risk
modeling. After a general overview of credit risk and standard
credit derivatives, the authors provide a short introduction into
Levy processes in general. This material is then used to study
single-name credit derivatives. Following this, the authors
introduce into firm-value Levy models, including the Merton model,
Black-Cox model, Levy first passage model, variance gamma model and
the one sided Levy default model. The problem of calibration is
discussed. After that, the authors introduce intensity Levy models
such as the Jarrow and Turnbull model, the Cox model and the
intensity-OU model. Multivariate credit products, collateralized
debt obligations and multivariate index modeling are discussed in
the following. In the final part of their book, the authors study
credit CPPIs and CPDOs as well as asset-backed securities."
(Zentralblatt MATH, 2010)