Structural Counterparty Risk Valuation for Credit Default Swaps

The valuation of counterparty risk for single-name credit derivatives is often based on reduced models where defaults intensities drive the jump-to-default of the counterparty. Whereas efficient and relatively easy to calibrate to credit default swaps (CDS) spreads and market data, we argue that this approach should be supplemented by the structural approach familiar in multiname credit risk (e.g., in the Gaussian copula models or in many widespread credit portfolios risk assessment tools). We discuss Merton-type structural models for counterparty risk, their advantages, soundness, and potential shortcomings, and address the question of their numerical tractability.We focus then on the derivation of closed formulas for counterparty risk on a (possibly collateralized) CDS--extending the ones familiar in the pricing of multiname barrier options. Most of our results are meaningful more generally for derivatives on two default-prone assets: multiple barrier conditions or equity-to-credit modeling.