Efficient computation of various valuation adjustments under local Lévy models
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.
|Keywords||BSDE, Characteristic function, CVA, Fast Fourier transform, XVA|
|Journal||SIAM Journal on Financial Mathematics|
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