A deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options
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| Format: | Preprint |
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2025
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| _version_ | 1866929718033383424 |
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| author | Negyesi, Balint Oosterlee, Cornelis W. |
| author_facet | Negyesi, Balint Oosterlee, Cornelis W. |
| contents | A deep BSDE approach is presented for the pricing and delta-gamma hedging of high-dimensional Bermudan options, with applications in portfolio risk management. Large portfolios of a mixture of multi-asset European and Bermudan derivatives are cast into the framework of discretely reflected BSDEs. This system is discretized by the One Step Malliavin scheme (Negyesi et al. [2024, 2025]) of discretely reflected Markovian BSDEs, which involves a $Γ$ process, corresponding to second-order sensitivities of the associated option prices. The discretized system is solved by a neural network regression Monte Carlo method, efficiently for a large number of underlyings. The resulting option Deltas and Gammas are used to discretely rebalance the corresponding replicating strategies. Numerical experiments are presented on both high-dimensional basket options and large portfolios consisting of multiple options with varying early exercise rights, moneyness and volatility. These examples demonstrate the robustness and accuracy of the method up to $100$ risk factors. The resulting hedging strategies significantly outperform benchmark methods both in the case of standard delta- and delta-gamma hedging. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_11706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options Negyesi, Balint Oosterlee, Cornelis W. Computational Finance Risk Management 91G20, 68T07, 91G60, 65C30 A deep BSDE approach is presented for the pricing and delta-gamma hedging of high-dimensional Bermudan options, with applications in portfolio risk management. Large portfolios of a mixture of multi-asset European and Bermudan derivatives are cast into the framework of discretely reflected BSDEs. This system is discretized by the One Step Malliavin scheme (Negyesi et al. [2024, 2025]) of discretely reflected Markovian BSDEs, which involves a $Γ$ process, corresponding to second-order sensitivities of the associated option prices. The discretized system is solved by a neural network regression Monte Carlo method, efficiently for a large number of underlyings. The resulting option Deltas and Gammas are used to discretely rebalance the corresponding replicating strategies. Numerical experiments are presented on both high-dimensional basket options and large portfolios consisting of multiple options with varying early exercise rights, moneyness and volatility. These examples demonstrate the robustness and accuracy of the method up to $100$ risk factors. The resulting hedging strategies significantly outperform benchmark methods both in the case of standard delta- and delta-gamma hedging. |
| title | A deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options |
| topic | Computational Finance Risk Management 91G20, 68T07, 91G60, 65C30 |
| url | https://arxiv.org/abs/2502.11706 |