Bilateral counterparty risk under funding constraints-Part II: CVA

Abstract

The correction in value of an over-the-counter derivative contract due to counterparty risk under funding constraints is represented as the value of a dividend-paying option on the value of the contract clean of counterparty risk and excess funding costs. This representation allows one to analyze the structure of this correction, the so-called Credit Valuation Adjustment (CVA for short), in terms of replacement cost/benefits, credit cost/benefits, and funding cost/benefits. We develop a reduced-form backward stochastic differential equations (BSDE) approach to the problem of pricing and hedging the CVA. In the Markov setup, explicit CVA pricing and hedging schemes are formulated in terms of semilinear partial differential equations.