Arbitrage-Free Pricing of XVA - Part I: Framework and Explicit Examples

35 Pages Posted: 24 Jan 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 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

Bichuch, Maxim and Capponi, Agostino and Sturm, Stephan, Arbitrage-Free Pricing of XVA - Part I: Framework and Explicit Examples (August 14, 2016). Available at SSRN: https://ssrn.com/abstract=2554600 or http://dx.doi.org/10.2139/ssrn.2554600

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

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