  The current research 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,
we 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, we can derive the
functional relation between expected recovery rate and default probability.
This relation depends on a single parameter only. In Monte Carlo simulations we
find that the same functional dependence also holds for jump-diffusion and
GARCH processes. We discuss how to incorporate this structural recovery rate
into reduced form models, in order to restore essential structural information
which is usually neglected in the reduced-form approach.
