Efficient Computation of Various Valuation Adjustments Under Local Lévy Models

25 Pages Posted: 18 Oct 2016 Last revised: 20 Aug 2018

See all articles by Anastasia Borovykh

Anastasia Borovykh

University of Bologna - Department of Mathematics

Andrea Pascucci

University of Bologna - Department of Mathematics

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: August 20, 2018

Abstract

Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local Lévy model: this framework includes a local volatility function and a local jump measure. Due to the unavailability of the characteristic function for such processes, we use an asymptotic approximation based on the adjoint formulation of the problem.

Keywords: Fast Fourier Transform, CVA, XVA, BSDE, Characteristic Function

JEL Classification: C02,G32

Suggested Citation

Borovykh, Anastasia and Pascucci, Andrea and Oosterlee, Cornelis W., Efficient Computation of Various Valuation Adjustments Under Local Lévy Models (August 20, 2018). Available at SSRN: https://ssrn.com/abstract=2853613 or http://dx.doi.org/10.2139/ssrn.2853613

Anastasia Borovykh (Contact Author)

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Andrea Pascucci

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

HOME PAGE: http://www.dm.unibo.it/~pascucci

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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