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Efficient Computation of Various Valuation Adjustments Under Local L\'evy Models

Anastasia Borovykh, Andrea Pascucci and Cornelis Oosterlee

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Abstract: 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 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.

Date: 2019-05
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Published in SIAM Journal on Financial Mathematics 9 (1), 251-273, 2018

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