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 Ri that is greater or less than R depending on its level of subordination. In general the Ri 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 Ri 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 Ri(R) and explore how correlations between the default probability and the recovery fractions Ri(R) influence the par spreads for credit default swaps. This scenario captures the effect of debt cushion on recovery fractions.