Efficient Computation of Various Valuation Adjustments Under Local Lévy Models
25 Pages Posted: 18 Oct 2016 Last revised: 20 Aug 2018
Date Written: August 20, 2018
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
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