Robust XVA

Forthcoming, Mathematical Finance

45 Pages Posted: 27 Feb 2018 Last revised: 23 Feb 2020

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: February 22, 2020

Abstract

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the super-replicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the close-out value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA.

Keywords: robust XVA, counterparty credit risk, backward stochastic differential equation, arbitrage-free valuation

JEL Classification: G13, C32

Suggested Citation

Bichuch, Maxim and Capponi, Agostino and Sturm, Stephan, Robust XVA (February 22, 2020). Forthcoming, Mathematical Finance, Available at SSRN: https://ssrn.com/abstract=3124586 or http://dx.doi.org/10.2139/ssrn.3124586

Maxim Bichuch

Johns Hopkins University ( email )

Baltimore, MD 20036-1984
United States

Agostino Capponi (Contact Author)

Columbia University ( email )

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

Stephan Sturm

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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