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

by Damiano Brigo of Fitch Solutions & Imperial College, and
Naoufel El-Bachir of the University of Reading

December 22, 2008

Abstract: We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consistently. We show with numerical experiments that the model implies plausible volatility smiles.

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.

Published in: Mathematical Finance, Vol. 20, No. 3, (July 2010), pp. 365-382.

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