Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model

22 Pages Posted: 8 Dec 2006

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Naoufel El-Bachir

University of Reading - ICMA Centre

Date Written: December 2006

Abstract

We present a two-factor stochastic default intensity and interest rate model for pricing single-name default swaptions. The specific positive square root processes considered fall in the relatively tractable class of affine jump diffusions while allowing for inclusion of stochastic volatility and jumps in default swap spreads. The parameters of the short rate dynamics are first calibrated to the interest rates markets, before calibrating separately the default intensity model to credit derivatives market data. A few variants of the model are calibrated in turn to market data, and different calibration procedures are compared. Numerical experiments show that the calibrated model can generate plausible volatility smiles. Hence, the model can be calibrated to a default swap term structure and few default swaptions, and the calibrated parameters can be used to value consistently other default swaptions (different strikes and maturities, or more complex structures) on the same credit reference name.

Keywords: Credit Derivatives, Credit Default Swap, Credit Default Swaption, Jump-Diffusion, Stochastic Intensity, Doubly Stochastic Poisson Process, Cox Process

JEL Classification: C15, C63, C65, G12, G13

Suggested Citation

Brigo, Damiano and El-Bachir, Naoufel, Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model (December 2006). Available at SSRN: https://ssrn.com/abstract=950208 or http://dx.doi.org/10.2139/ssrn.950208

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Naoufel El-Bachir (Contact Author)

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading RG6 6BA
United Kingdom

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