Feynman Kac for Functional Jump Diffusions with an Application to Credit Value Adjustment

15 Pages Posted: 26 Sep 2014 Last revised: 22 Jun 2015

See all articles by Eduard Kromer

Eduard Kromer

University of California, Berkeley

Ludger Overbeck

University of Giessen

Jasmin Röder

University of Giessen

Date Written: June 19, 2015

Abstract

We provide a proof for the functional Feynman-Kac Theorem for jump diffusions with path-dependent coefficients. To obtain this result we first study the existence and uniqueness of solutions to functional jump diffusions and derive a useful bound for the solution. We apply our results to the problem of Credit Value Adjustment (CVA) in a bilateral counterparty risk framework. We derive the corresponding functional CVA-PIDE and extend existing results on CVA to a setting which enables the pricing of path-dependent derivatives.

Keywords: Functional Feynman-Kac Theorem, functional Ito formula, functional jump diffusion, path-dependent coefficients, Credit Value Adjustment, bilateral counterparty risk, path-dependent derivatives, Asian option

JEL Classification: G13, C63

Suggested Citation

Kromer, Eduard and Overbeck, Ludger and Röder, Jasmin, Feynman Kac for Functional Jump Diffusions with an Application to Credit Value Adjustment (June 19, 2015). Available at SSRN: https://ssrn.com/abstract=2500782 or http://dx.doi.org/10.2139/ssrn.2500782

Eduard Kromer

University of California, Berkeley ( email )

Evans Hall
Berkeley, CA 3860 94720
United States

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

Jasmin Röder (Contact Author)

University of Giessen ( email )

Arndtstr. 2
Giessen, 35392
Germany

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