2002b): Pricing and Hedging Vulnerable Credit Derivatives with Copulas, Working

In this paper we apply a copula function pricing technique to the eval-uation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable to separate the specifi-cation of marginal default probabilities from their dependence structure. Their use is based here on no-arbitrage arguments, which provide pricing bounds and easy-to-implement super-replication strategies. At a second stage, we specify the copula function to be a mixture one. In this case, we obtain closed form prices and hedges, which we calibrate on real market data. For the sake of comparison, we add a Clayton calibration. Copula functions have been suggested for the evaluation of credit derivatives by Li (2000). Li uses the notion of survival time or time until default and studies the joint distribution of times to default for different entities. He exploits the possibility of writing any joint distribution function as a copula, taking as arguments the marginal distributions, in order to specify the joint default probabilities required for credit derivative pricing. Copulas allow him to split the specification of the joint default arrival into two steps: first model (and calibrate) the marginal default probabilities, then specify their dependence. In particular, he shows that the Riskmetrics approach is equivalent to adopting a very specific copula, namely the Gaussian one. Schönbucher and Schubert (2001) have expanded Li’s idea in the context of reduced form models. They have used copulas also in order to represen