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We introduce the general arbitrage-free valuation framework for counterpartyrisk adjustments in presence of bilateral default risk, including default ofthe investor. We illustrate the symmetry in the valuation and show that theadjustment involves a long position in a put option plus a short position in acall option, both with zero strike and written on the residual net value of thecontract at the relevant default times. We allow for correlation between thedefault times of the investor, counterparty and underlying portfolio riskfactors. We use arbitrage-free stochastic dynamical models. We then specializeour analysis to Credit Default Swaps (CDS) as underlying portfolio,generalizing the work of Brigo and Chourdakis (2008) [5] who deal withunilateral and asymmetric counterparty risk. We introduce stochastic intensitymodels and a trivariate copula function on the default times exponentialvariables to model default dependence. Similarly to [5], we find that bothdefault correlation and credit spread volatilities have a relevant andstructured impact on the adjustment. Differently from [5], the two parties willnow agree on the credit valuation adjustment. We study a case involving BritishAirways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateraladjustments in concrete crisis situations.

Bilateral Counterparty Risk Valuation with Stochastic Dynamical Models and Application to Credit Default Swaps