Debt Subordination and The Pricing of Credit Default Swaps

First passage models, where corporate assets undergo a random walk and default occurs if the assets fall below a threshold, provide an attractive framework for modeling the default process. Recently such models have been generalized to allow a fluctuating default threshold or equivalently a fluctuating total recovery fraction $R$. For a given company a particular type of debt has a recovery fraction $R_i$ that is greater or less than $R$ depending on its level of subordination. In general the $R_i$ are functions of $R$ and since, in models with a fluctuating default threshold, the probability of default depends on $R$ there are correlations between the recovery fractions $R_i$ and the probability of default. We find, using a simple scenario where debt of type $i$ is subordinate to debt of type $i-1$, the functional dependence $R_i(R)$ and explore how correlations between the default probability and the recovery fractions $R_i(R)$ influence the par spreads for credit default swaps. This scenario captures the effect of debt cushion on recovery fractions.