Jumps in Intensity Models

by Jessica Cariboni of European Commission--Joint Research Centre and Katholieke Universiteit Leuven, and
Wim Schoutens of Katholieke Universiteit Leuven

May 4, 2006

Abstract: This work presents intensity-based credit risk models where the default intensity of the point process is modeled by an Ornstein-Uhlenbeck type process completely driven by jumps. Under this model we compute the default probability over time by linking it to the characteristic function of the integrated intensity process. In case of the Gamma and Inverse Gaussian Ornstein-Uhlenbeck processes this leads to a closed form expression for the default probability and to a straightforward estimate of credit default swaps prices. The model is calibrated to a series of real-market term structures. Results are compared with the well known cases of Poisson and CIR dynamics. Possible extensions of the model to the multivariate setting are finally discussed.

JEL Classification: C60.

Keywords: Ornstein-Uhlenbeck process, default probability, intensity model, CDS, jumps.

Published in: Metrika, Vol. 69, No. 2-3, (March 2009), pp. 173-198.

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