关键词: 期权定价, 行为金融学, 行为期权定价, 随机波动率模型, 深度学习

Abstract: 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.

Key words: option pricing, behavioral finance, behavioral option pricing, stochastic volatility model, deep learning