An Exact Formula for Default Swaptions Pricing in the SSRJD Stochastic Intensity Model

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An Exact Formula for Default Swaptions Pricing in the SSRJD Stochastic Intensity Model

by Damiano Brigo of Q-SCI, DerivativeFitch, and
Naoufel El-Bachir of University of Reading

November 8, 2007

Abstract: We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of the shifted square root jump diffusion (SSRJD) default intensity model. The formula consists of a decomposition of an option on a summation of survival probabilities in a summation of options on the underlying survival probabilities, where the strike for each option is adjusted.

JEL Classification: C63, C65, G12, G13.

Keywords: Credit derivatives, Credit Default Swap, Credit Default Swaption, Jump-diffusion, Stochastic intensity, Doubly stochastic Poisson process, Cox process, Semi-Analytic formula, Numerical integration.

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