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

Abstract

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 At defines the default trigger and the recovery risk driver Rt 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.