Counterparty Risk for CDS : Default Clustering Effects

We derive a closed-form expression for the bilateral credit valuation adjustment of a credit default swap in presence of simultaneous defaults. We develop our analysis under a default intensity model specified by a class of three-dimensional subordinators, allowing for default dependence through common risk factors. Due to simultaneous default occurrences, the joint conditional survival probability of default times consists of both an absolutely continuous and a singular part. We explicitly characterize the corresponding densities, and perform a suitable decomposition yielding the counterparty risk prices. Our analysis indicates that simultaneous defaults have material impact on the size and directionality of the adjustments. Our findings suggest policymakers to consider default clustering when designing counterparty valuation procedures, especially during periods of financial distress