Dependence Of Defaults And Recoveries In Structural Credit Risk Models
The current paper on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite of their pronounced effect on the tail of the loss distribution. Here, the authors take a step back, historically, and start again from the Merton model, where defaults and recoveries are both determined by an underlying process. Hence, they are intrinsically connected. For the diffusion process, they can derive the functional relation between expected recovery rate and default probability. This relation depends on a single parameter only. In Monte Carlo simulations they find that the same functional dependence also holds for jump-diffusion and GARCH processes.