Following a direct data-driven approach, we propose a robust encoder-decoder Gated Recurrent Unit (GRU), ${\text{GRU}}_{\delta }$, for optimal discrete option hedging. The proposed ${\text{GRU}}_{\delta }$ utilizes the Black-Scholes model as a pre-trained model and incorporates sequential information and feature selection. Using the S&P 500 index European option market data, we demonstrate that the weekly and monthly hedging performance of the proposed ${\text{GRU}}_{\delta }$ significantly surpasses that of the data-driven minimum variance (MV) method, the regularized kernel data-driven model, and the SABR-Bartlett method. In addition, the daily hedging performance of the proposed ${\text{GRU}}_{\delta }$ also surpasses that of MV methods based on parametric models, the kernel method, and SABR-Bartlett method.

遵循直接数据驱动的方法，我们提出了一个强大的编码器-解码器门控循环单元（GRU）， ${\text{格鲁乌}}_{\delta }$, 最佳离散期权对冲。拟议的${\text{格鲁乌}}_{\delta }$利用 Black-Scholes 模型作为预训练模型，并结合了序列信息和特征选择。使用标准普尔 500 指数欧洲期权市场数据，我们证明了所提议的每周和每月对冲表现${\text{格鲁乌}}_{\delta }$显着超过数据驱动的最小方差（MV）方法、正则化核数据驱动模型和 SABR-Bartlett 方法。此外，建议的每日对冲表现${\text{格鲁乌}}_{\delta }$ 也超过了基于参数模型的 MV 方法、核方法和 SABR-Bartlett 方法。