Various valuation adjustments (XVAs) can be written in terms of nonlinear partial integro-differential equations equivalent to forward-backward SDEs (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.

BSDE, Characteristic function, CVA, Fast Fourier transform, XVA
dx.doi.org/10.1137/16M1099005
SIAM Journal on Financial Mathematics
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Borovykh, A.I, Pascucci, A, & Oosterlee, C.W. (2018). Efficient computation of various valuation adjustments under local Lévy models. SIAM Journal on Financial Mathematics, 9(1), 251–273. doi:10.1137/16M1099005