  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.

Condensed Matter