Arbitrage-Free Pricing of XVA – Part II: PDE Representation and Numerical Analysis
18 Pages Posted: 23 Feb 2015 Last revised: 15 Aug 2016
Date Written: August 14, 2016
We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer’s and seller’s XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We show the existence of a unique classical solution to the PDE by first proving the existence and uniqueness of a viscosity solution and then its regularity. We use the uniqueness result to conduct a thorough numerical study illustrating how funding costs, repo rates, and counterparty credit risk contribute to determine the total valuation adjustment.
Keywords: XVA, counterparty credit risk, funding spreads, partial differential equations, viscosity and classical solutions
JEL Classification: G13, C32
Suggested Citation: Suggested Citation