Fast Valuation and Calibration of Credit Default Swaps Under Levy 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.With this method we calibrate two well known\levy\models, the Normal Inverse Gaussian and the CGMY, to the market quotes of the iTraxx Series 7 and 8 constituents. In the calibration study we look at the root mean square error of the fit and find that both models give a very good fit to market data. Furthermore, we investigate how the out of calibration given parameters evolve over the year covered by the two series. Finally, we look at the changes in the default probability term structure over the year.