Arbitrage-Free Pricing of XVA – Part II: PDE Representation and Numerical Analysis

18 Pages Posted: 23 Feb 2015 Last revised: 15 Aug 2016

See all articles by Maxim Bichuch

Maxim Bichuch

Johns Hopkins University

Agostino Capponi

Columbia University

Stephan Sturm

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences

Date Written: August 14, 2016

Abstract

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

Bichuch, Maxim and Capponi, Agostino and Sturm, Stephan, Arbitrage-Free Pricing of XVA – Part II: PDE Representation and Numerical Analysis (August 14, 2016). Available at SSRN: https://ssrn.com/abstract=2568118 or http://dx.doi.org/10.2139/ssrn.2568118

Maxim Bichuch

Johns Hopkins University ( email )

Baltimore, MD 20036-1984
United States

Agostino Capponi

Columbia University ( email )

S. W. Mudd Building
New York, NY 10027
United States

Stephan Sturm (Contact Author)

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences ( email )

United States
5088315921 (Phone)
5088315824 (Fax)

HOME PAGE: http://users.wpi.edu/~ssturm

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
138
Abstract Views
847
rank
258,696
PlumX Metrics