Bilateral counterparty risk with application to CDSs

Previous research on credit valuation adjustments (CVAs) with correlation between underlying and counterparty default, including volatilities of both, assumed unilateral default risk. However, the crisis prompted counterparties to ask institutions to calculate CVAs by taking into account the institutions’ own defaults. Here, Damiano Brigo and Agostino Capponi build a rigorous arbitrage-free framework for bilateral (symmetric) CVAs and apply it to credit default swaps

In the valuation arena, bilateral features are relevant for counterparty risk and can often be responsible for seemingly paradoxical statements. For example, Citigroup, in its press release on its first-quarter 2009 revenues, reported a positive mark-to-market due to its worsened credit quality: “Revenues also included... a net $2.5 billion positive credit valuation adjustment (CVA) on derivative positions, excluding monolines, mainly due to the widening of Citi’s credit default swap (CDS)