Valuation of Credit Default Swaps with Wrong Way Risk – Model Implementation and a Computational Tune-Up

In their work, Brigo and Capponi (2010) introduce a numerical approach for calculating credit valuation adjustments (CVA) for credit default swaps (CDS). In contrast to previous research, they consider the default of the party doing the calculation, and its correlation to the defaults of the counterparty and the reference entity. Assuming bilateral counterparty credit risk, this approach generates symmetric and arbitrage free CVA. The most elaborate part of this computation is the generation of the default probability structure of the reference entity conditional on the default of either the investor or the counterparty. Brigo and Capponi (2010) suggest the use of the Fractional Fourier Transformation (FRFT) technique for this purpose. In this paper, we introduce the precise and practical algorithm for this numerical approach and display the steps needed for the FRFT technique. In addition, we offer a computational tune-up for the calculation of the conditional value of the CDS through a lognormal approximation. Throughout a variety of examples we show that this robust approximation delivers satisfying results, while requiring less computational power and less excessive implementation than the FRFT approach.