Studying on the hedging strategies of basket default swaps under stochastic recovery environment

We provide the hedging strategies of basket default swaps with respect to actively credit default swap index. Based upon the Laurent´s model, the extended model in which recovery is not constant but stochastic recovery depending upon the number of defaults in the portfolio is derived. We also develop the calibration procedure of such recovery rate form onto market input. Under the stochastic recovery environment, we study the hedging strategies of basket default swaps, such as the first-to-default swap and n-th default swap. We provide some numerical experiments including computing of the hedging strategies of first-to-default contract and n-th default swap contract and comparing the hedging results of [0-3%] collateralized debt obligations (CDO) tranche and [12-20%] CDO tranche between Laurent´s model and the extended model. The numerical results show that the hedging strategies of basket default swap contract are feasible and the influences of recovery rate on the hedging strategies are not neglected whatever the portfolio credit derivatives.