用神经网络加速美式期权定价，比传统方法更快更准。
Time Deep Gradient Flow Method for pricing American options
- 用时间深度梯度流方法处理美式期权的自由边界问题
- 在五维情况下精度高，训练速度优于Deep Galerkin方法
- 适合金融工程中高维期权定价场景
本研究探索基于神经网络的方法，在Black-Scholes与Heston模型下对多维美式看跌期权进行定价，最高扩展至五维。重点比较了时间深度梯度流（TDGF）方法与深度迦辽金法（DGM）。通过改进采样策略，将TDGF方法拓展至处理美式期权固有的自由边界偏微分方程。两种方法均表现出高精度，且在计算速度上显著优于传统蒙特卡洛方法；其中TDGF在训练阶段表现更优。实验验证了该方法在五维情况下的有效性与高效性。
原文摘要 · Abstract (English)
In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow (TDGF) method and the Deep Galerkin Method (DGM). We extend the TDGF method to handle the free-boundary partial differential equation inherent in American options. We carefully design the sampling strategy during training to enhance performance. Both TDGF and DGM achieve high accuracy while outperforming conventional Monte Carlo methods in terms of computational speed. In particular, TDGF tends to be faster during training than DGM.
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