An Explicit Scheme for Pathwise XVA Computations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917573043421184 |
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| author | Abbas-Turki, Lokman Crépey, Stéphane Li, Botao Saadeddine, Bouazza |
| author_facet | Abbas-Turki, Lokman Crépey, Stéphane Li, Botao Saadeddine, Bouazza |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Explicit Scheme for Pathwise XVA Computations Abbas-Turki, Lokman Crépey, Stéphane Li, Botao Saadeddine, Bouazza Risk Management Numerical Analysis Computational Finance Machine Learning 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. |
| title | An Explicit Scheme for Pathwise XVA Computations |
| topic | Risk Management Numerical Analysis Computational Finance Machine Learning |
| url | https://arxiv.org/abs/2401.13314 |