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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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  • Balint Negyesi
  • Cornelis W. Oosterlee

Abstract

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 $\Gamma$ 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.

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  • Balint Negyesi & Cornelis W. Oosterlee, 2025. "A deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options," Papers 2502.11706, arXiv.org.
    • Handle: RePEc:arx:papers:2502.11706
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    References listed on IDEAS

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    1. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2020. "Pricing and Hedging American-Style Options with Deep Learning," JRFM, MDPI, vol. 13(7), pages 1-12, July.
    2. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2019. "Pricing and hedging American-style options with deep learning," Papers 1912.11060, arXiv.org, revised Jul 2020.
    3. Yangang Chen & Justin W. L. Wan, 2021. "Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 45-67, January.
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