An Explicit Scheme for Pathwise XVA Computations

Lokman Abbas-Turki, St\'ephane Cr\'epey, Botao Li and Bouazza Saadeddine
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Lokman Abbas-Turki: LPSM
St\'ephane Cr\'epey: LPSM
Botao Li: LPSM
Bouazza Saadeddine: LPSM, LaMME

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Abstract: Motivated by the equations of cross valuation adjustments (XVAs) in the realistic case where capital is deemed fungible as a source of funding for variation margin, we introduce a simulation/regression scheme for a class of anticipated BSDEs, where the coefficient entails a conditional expected shortfall of the martingale part of the solution. The scheme is explicit in time and uses neural network least-squares and quantile regressions for the embedded conditional expectations and expected shortfall computations. An a posteriori Monte Carlo validation procedure allows assessing the regression error of the scheme at each time step. The superiority of this scheme with respect to Picard iterations is illustrated in a high-dimensional and hybrid market/default risks XVA use-case.

Date: 2024-01
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