Levy Processes in Credit Risk
Published on 28. August 2009
200 pages
978-0-470-74903-6 (ISBN)
Description
This book is an introductory guide to using Lévy processes forcredit risk modelling. It covers all types of credit derivatives:from the single name vanillas such as Credit Default Swaps (CDSs)right through to structured credit risk products such asCollateralized Debt Obligations (CDOs), Constant ProportionPortfolio Insurances (CPPIs) and Constant Proportion DebtObligations (CPDOs) as well as new advanced rating models for AssetBacked Securities (ABSs).
Jumps and extreme events are crucial stylized features,essential in the modelling of the very volatile credit markets -the recent turmoil in the credit markets has once again illustratedthe need for more refined models.
Readers will learn how the classical models (driven by Brownianmotions and Black-Scholes settings) can be significantly improvedby using the more flexible class of Lévy processes. By doingthis, extreme event and jumps can be introduced into the models togive more reliable pricing and a better assessment of therisks.
The book brings in high-tech financial engineering models forthe detailed modelling of credit risk instruments, setting up thetheoretical framework behind the application of Lévy Processesto Credit Risk Modelling before moving on to the practicalimplementation. Complex credit derivatives structures such as CDOs,ABSs, CPPIs, CPDOs are analysed and illustrated with marketdata.
Reviews / Votes
"This text introduces into the use of Levy processes in credit riskmodeling. After a general overview of credit risk and standardcredit derivatives, the authors provide a short introduction intoLevy processes in general. This material is then used to studysingle-name credit derivatives. Following this, the authorsintroduce into firm-value Levy models, including the Merton model,Black-Cox model, Levy first passage model, variance gamma model andthe one sided Levy default model. The problem of calibration isdiscussed. After that, the authors introduce intensity Levy modelssuch as the Jarrow and Turnbull model, the Cox model and theintensity-OU model. Multivariate credit products, collateralizeddebt obligations and multivariate index modeling are discussed inthe following. In the final part of their book, the authors studycredit CPPIs and CPDOs as well as asset-backed securities."(Zentralblatt MATH, 2010)More details
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Wim Schoutens | Jessica Cariboni
Levy Processes in Credit Risk
Book
07/2009
Wiley
€140.50
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Persons
Wim Schoutens (Leuven, Belgium) is a research professor infinancial engineering in the Department of Mathematics at theCatholic University of Leuven, Belgium. He has extensive practicalexperience of model implementation and is well known for hisconsulting work in the banking industry. Wim is the author ofLévy Processes in Finance and co-editor of ExoticOption Pricing and Advanced Lévy Models both published byWiley. He teaches at 7city Learning and London Financial Studies.He is Managing Editor of the International Journal ofTheoretical and Applied Finance and Associate Editor ofMathematical Finance and Review of DerivativesResearch.
Jessica Cariboni (Ispra, Italy) has a PhD in appliedstatistics from the Catholic University of Leuven, Belgium. She wasa junior quantitative analyst at Nextra Investment Management. Sheis currently a functionary of the European Commission andresearcher at the European Commission DG-Joint Research Centre,Ispra, Italy. She is also co-author of the book GlobalSensitivity Analysis: The Primer published by Wiley.
Content
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.
