Local volatility and the recovery rate of credit default swaps

Credit default swap (CDS) spreads can only be decomposed into the probability of default and the loss-given-default by imposing some structure. Employing a hybrid binomial tree for equities and a recovery function, Das and Hanouna (2009) obtain accurate estimates for CDS spreads by fitting the model to historical equity volatilities. We extend their approach by including the full implied volatility surface, developing an implied binomial tree with a jump to default based on extending the Derman and Kani (1994) tree. We then evaluate the effect of including the full volatility surface on the implied CDS recovery rate.