Fast valuation and calibration of credit default swaps under Lévy dynamics

Abstract

In this paper we address the issue of finding an efficient and flexible numerical approach for calculating survival/default probabilities and pricing Credit Default Swaps under advanced jump dynamics. We have chosen to use the firm’s value approach, modeling the firm’s value by an exponential Levy model. For this approach the default event is defined as a first passage of a barrier and it is therefore possible to exploit a numerical technique developed to price barrier options under Levy models to calculate the default probabilities. The method presented is based on the Fourier-cosine series expansion of the underlying model’s density function