We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs)...

We analyze the market price of counterparty risk and develop an arbitrage-free pricing valuation framework, inclusive of collateral mitigation. We show that the adjustment is given by the sum of option payoff terms, depending on the netted exposure, i.e. the difference between the on-default...