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Pricing Credit Default Swaps under LÚvy Models

by Jessica Cariboni of the European Commission, and
Wim Schoutens of Katholieke Universiteit Leuven

November 22, 2004

Abstract: Most structural models for credit pricing assume Geometric Brownian motion to describe the firm asset value. However, the underlying lognormal distribution does not match empirical distributions, typically skewed and leptokurtic. Moreover, defaults are usually driven by shocks, which are not captured by the continuous paths of Brownian motion. We assume the asset price process is driven by a pure-jump LÚvy process and default is triggered by the crossing of a preset barrier. Our model incorporates asymmetry, fat-tail behaviour, jumps and instantaneous defaults. Under this model we price Credit Default Swaps, detailing the calculations for the Variance Gamma process.

AMS Classification: 60J75, 65C30.

Keywords: LÚvy process, survival probability, credit risk, structural model, credit default swap, barrier option.

Published in: Journal of Computational Finance, Vol. 10, No. 4, (Summer 2007), pp. 1-21.

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