Arbitrage-Free Pricing of XVA - Part I: Framework and Explicit Examples
35 Pages Posted: 24 Jan 2015 Last revised: 15 Aug 2016
Date Written: August 14, 2016
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) associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA which in turn identify a no-arbitrage interval. When borrowing and lending rates coincide we provide a fully explicit expression for the uniquely determined price of XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. This extends the result of Piterbarg by incorporating the effect of premature contract termination due to default risk of the trader and of his counterparty.
Keywords: XVA, counterparty credit risk, funding spreads, backward stochastic differential equations, arbitrage-free pricing, valuation adjustment
JEL Classification: G13, C32
Suggested Citation: Suggested Citation