Arbitrage-Free Pricing of XVA

Agostino Capponi (John Hopkins University)
Thursday, December 18, 2014 - 4:00pm
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We introduce a framework for computing the total valuation adjustment (XVA) of an European claim accounting for funding spreads, counterparty risk, and collateral mitigation. We use no-arbitrage arguments to derive the nonlinear backward stochastic differential equations (BSDEs) associated with the portfolios which replicate long and short positions in the claim. This leads to defining buyer and sellers? XVAs which in turn identify a no-arbitrage band. When borrowing and lending rates coincide, our framework reduces to a generalized Piterbarg's model. In this case, we provide a fully explicit expression for the uniquely determined price of XVA. When they differ, we derive the semi-linear partial differential equations (PDEs) associated with the non-linear BSDEs. We use them to conduct a numerical analysis showing high sensitivity of the no-arbitrage band and replicating strategies to funding spreads and collateral levels.

This is joint work with Stephan Sturm and Maxim Bichuch.