Efficient XVA Computation under Local Lévy Models

Anastasia Borovykh, Andrea Pascucci, Cornelis W. Oosterlee: Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FB-SDEs. 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 L ́evy 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.