深度学习能解决美式障碍期权定价中的“维度诅咒”问题吗？——基于行为期权的视角

Can Deep Learning Method Solve “Curse of Dimesionality” in American Barrier Option Pricing?—Based on the Perspective of Behavioral Option

摘要: 为了刻画投资者行为对金融资产价格的影响，本文采用行为资产定价模型来刻画风险资产价格的动态变化，以深度学习方法为美式障碍期权定价，并与传统的最小二乘蒙特卡洛法进行比较。数值实验结果表明，深度学习法不仅在单资产表现出色，而且在高维资产定价上仍然具有高精度、高效率的特点，避免了传统方法因“维度爆炸”导致无法定价的问题。本文的研究结论完善了行为资产模型下的期权定价理论体系，为其他产品的定价提供借鉴与思路。

Abstract: In order to capture the features of investor behavior on financial asset prices, in this paper, we use behavioral asset pricing model to describe the dynamic change of risk asset price, use deep learning method to price American barrier options, and compare it with traditional least squares Monte Carlo approach. Numerical experimental result shows that deep learning method not only performs well in single assets, but also has the characteristics of high precision and high efficiency in high-dimensional asset pricing, avoiding the problem that traditional methods cannot price due to “dimension explosion”. Our research results improve the theoretical system of option pricing under the behavioral asset pricing model, and provide reference and ideas for the pricing of other products.