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.

Additional Metadata
Keywords BSDE, Characteristic function, CVA, Fast Fourier transform, XVA
Persistent URL dx.doi.org/10.1137/16M1099005
Journal SIAM Journal on Financial Mathematics
Citation
Borovykh, A, 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