基于深度学习算法的行为期权定价

针对一类考虑了投资者微观结构随机变迁、投资者行为存在羊群效应以及非理性情绪的高维行为资产价格模型，推导出行为期权定价偏微分方程，构建了基于深度学习算法的行为期权定价方法：首先，基于费曼卡兹公式推导出行为期权价格的迭代方程；然后，用神经网络来逼近迭代方程中的期权价格关于标的模型空间变量的梯度函数；最后，通过深度神经网络参数寻优得到期权价格。数值实验表明：相比蒙特卡洛方法，深度学习算法在计算高维标的资产的期权价格时，获得的结果不仅精度更好，而且效率更高；在相同精度要求下，深度学习算法所需要的仿真路径数更少。研究发现：市场中投资者的非理性情绪程度越严重，期权价格越高；股市微观结构调整速度和羊群效应，对不同成熟度的市场上期权价格的影响，存在异质性：在不成熟市场上，股市微观结构调整速度越快，投资者的羊群效应越严重，期权价格越高；而对于成熟市场，投资者结构回复长期均衡以及羊群效应，均起到稳定期权价格的作用。

Behavioral Option Pricing Based on Deep-Learning Algorithm

This paper proposes a deep-learning algorithm based the behavioral option pricing approach, under a real high-dimensional behavioral asset pricing model considering the herding behavior, restricted rationality, and stochastically developing structure of investors. This approach uses the Feynman-Kac formula to derive an iterative equation of option price, and approximates the gradient functions in the iterative equation by neural network. The option price is obtained by optimizing the parameters of the whole deep-learning neural network. The numerical experiments show that compared with the Monte Carlo method, the deep-learning neural network is not only more accurate but also more efficient when valuating options with high-dimensional behavioral assets. The research finds that the option price is generally increasing in the investors’ irrationality of stock market. The effects of market micro-structure reversion speed and investors’ herding behavior on option price are heterogeneous with respect to markets in different maturities. For an immature market, the option price is increasing in the reversion speed and herding behavior while for a mature market, both factors stabilize the option price.