Default Swaps and Hedging of Credit Baskets

We investigate the pricing of basket cedit derivatives and their hedging with single name credit default swaps (CDS). The market in credit default swaps quotes fair insurance premiums whose dynamics is the antural starting point of our model. Pricing basket credit derivatives requires a model for the dependencies between the default times. In case of a pure jump filtration, dependencies are characterized by default implied spread changes. In this setup we derive a simple system of integral equations involving the notional amounts of the dynamic hedge positions, the price and the spread of a basket derivative. We provide some numerical examples of explicit hedging strategies and valuations of first-to-default baskets illustrating the approach.