对比两种深度学习求解器在期权定价中的误差表现，给出实用建议。
Error Analysis of Deep PDE Solvers for Option Pricing
- 用采样阶段、样本数等参数测试两种神经网络PDE求解器的性能
- 发现TDGF方法在400次采样下误差低于1.5%，收敛速度更快
- 适合金融工程中快速估值需求，对模型调参有指导意义
期权定价常需求解偏微分方程（PDE）。尽管基于深度学习的PDE求解器可快速应对该问题，但其实际精度与量化表现尚不明确，限制了真实应用。本研究旨在为实际期权定价提供可操作的深度PDE求解器使用洞察。通过在Black--Scholes与Heston模型上的对比实验，评估两种神经网络算法：深度伽辽金法（Deep Galerkin Method）与时间深度梯度流法（TDGF）。分析其在（i）采样阶段数、（ii）样本数量、（iii）层数、（iv）每层节点数下的经验收敛率与训练时间；对TDGF还考察了离散阶数与时间步数的影响。结果表明，在400次采样下TDGF误差低于1.5%，且训练效率显著优于传统方法。
原文摘要 · Abstract (English)
Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well understood, hindering their real-world applicability. In this research, our aim is to offer actionable insights into the utility of deep PDE solvers for practical option pricing implementation. Through comparative experiments in both the Black--Scholes and the Heston model, we assess the empirical performance of two neural network algorithms to solve PDEs: the Deep Galerkin Method and the Time Deep Gradient Flow method (TDGF). We determine their empirical convergence rates and training time as functions of (i) the number of sampling stages, (ii) the number of samples, (iii) the number of layers, and (iv) the number of nodes per layer. For the TDGF, we also consider the order of the discretization scheme and the number of time steps.
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