Bond and CDS Pricing with Recovery Risk II : The Stochastic Recovery Black-Cox Model

Building on recent work incorporating recovery risk into structural models we consider the Black-Cox model with an added recovery risk driver. The recovery risk driver arises naturally in the context of imperfect information implicit in the structural framework. This leads to a two-factor structural model we call the Stochastic Recovery Black-Cox model, whereby the asset risk driver A_t defines the default trigger and the recovery risk driver R_t defines the amount recovered in the event of default. We then price zero-coupon bonds and credit default swaps under the Stochastic Recovery Black-Cox model. Introducing separate but correlated risk drivers leads to a decoupling of the default and recovery risk premiums in the credit spread. Finally, we compare our results with the classic Black-Cox model and give explicit expressions for the recovery risk premium in the Stochastic Recovery Black-Cox model