一种用于由高维多资产百慕大期权构成的大型投资组合同时定价与 delta-gamma 对冲的深度 BSDE 方法
A deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options
AI总结：
提出基于离散反射 BSDE、One Step Malliavin 格式与神经网络回归 Monte Carlo 的深度方法，实现高维多资产百慕大期权大型投资组合的联合定价及 delta-gamma 对冲。
摘要：
本文提出一种深度 BSDE 方法，用于高维百慕大期权的定价和 delta-gamma 对冲，并应用于投资组合风险管理。由多资产欧式与百慕大衍生品混合构成的大型投资组合被纳入离散反射 BSDE 框架。该系统通过离散反射 Markovian BSDE 的 One Step Malliavin 格式（Negyesi 等人 [2024, 2025]）进行离散化，其中包含一个 Γ 过程，对应于相关期权价格的二阶敏感度。离散化系统采用神经网络回归 Monte Carlo 方法求解，能够针对大量标的资产高效计算。所得期权 Deltas 与 Gammas 被用于对相应复制策略进行离散再平衡。本文在高维一篮子期权以及由多个具有不同提前行权权利、货币性和波动率的期权构成的大型投资组合上开展了数值实验。这些算例证明了该方法在多达 100 个风险因子时的稳健性和准确性。在标准 delta 对冲和 delta-gamma 对冲情形下，所得对冲策略均显著优于基准方法。
英文摘要：
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.
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