Fast Valuation and Calibration of Credit Default Swaps Under Lévy Dynamics

Credit default swaps (CDSs), the basic building block of the credit risk market, offer investors the opportunity to either buy or sell default protection on a reference entity. The protection buyer pays a premium periodically for the possibility to get compensation if there is a credit event on the reference entity until maturity or the default time, which ever is first. If there is a credit event the protection seller covers the losses by returning the par value. The premium payments are based on the CDS spread. The spread of CDSs depends on the default probability of the underlying reference entity and it is possible to back out the market view of default probabilities for individual names from quoted market prices. It is therefore essential to be able to use advanced models in credit default modeling. Lately Lévy models have attracted attention in the field of credit risk, see e.g. Cariboni (2007), Cariboni and Schoutens (2007) and Madan and Schoutens (2007). Cariboni and Schoutens (2007) price CDSs using the structural approach with a Variance Gamma model driving the firm value. To calculate the default probabilities they derive the partial integro-differential equation (PIDE) satisfied by the barrier option price and solve the equation by adapting a numerical scheme developed Delft University of Technology, Delft Institute of Applied Mathematics, Delft, the Netherlands, E-mail: [email protected] EURANDOM, Eindhoven University of Technology, Eindhoven, the Netherlands. E-mail: [email protected], CWI Centrum Wiskunde & Informatica, Amsterdam, the Netherlands, E-mail: [email protected], and Delft University of Technology, Delft Institute of Applied Mathematics, Delft, the Netherlands Research Professor, K.U.Leuven, Department of Mathematics, Leuven, Belgium. E-mail: [email protected]