Numerical methods to quantify the model risk of basket default swaps

The valuation of basket default swaps depends crucially on the joint default probability of the underlying assets in the basket. It is known that this probability can be modeled by means of a copula function which links the marginal default probabilities to a joint probability. The valuation bears risk due to the uncertainty of the copula, the relation of the assets to each other and the marginal distributions which we call together the model risk. To value basket default swaps and to compute model risk parameters we present an efficient numerical approach based on importance sampling and applicable to different classes of copula models. Our numerical findings show that the choice of the underlying copula model influences strongly the risk profile of the basket and should be tailored advisedly.