Abstract: With the rapid development of the new generation of information technology, AI methods have been widely used in many areas of the financial industry, such as asset pricing, investment portfolio, algorithmic trading, risk management, credit approval and fraud detection. At present, benefiting from the computing power and predictive performance of AI technology, many financial institutions or government regulators are beginning to use AI technology (including machine learning) to improve the efficiency of their daily operations. In recent years, with the popularization of massively parallel computing and GPU devices, the computing power of computers has been greatly improved. In addition, the scale of data available for machine learning is growing. Therefore, thanks to an increase in data, the enhancement of computing power, the maturity of learning algorithms and the richness of application scenarios, deep learning methods based on neural networks have improved and developed rapidly. As we all know, option is one of the most important derivatives in risk management practice such as hedging risk and hedging. With the wide application of derivatives in risk transfer in financial markets, the accurate and efficient pricing of options has become the most important and challenging key scientific problems in modern financial economics. At present, a large number of scholars have begun to turn to the application of deep learning in the field of financial derivative pricing.
The deep learning method is introduced into European option pricing in this paper, which constructs a data-driven non-parametric option pricing model based on deep neural network. The empirical research is conducted using the sample data of SSE 50ETF call options and put options, and a comparative analysis is made with the classical Black-Scholes model. Specifically, from the perspective of root mean square error, the DNN model improves the pricing power of SSE 50ETF call options by 76.97% compared to the BS model, while for put options it improves by 70.27%. From the perspective of average absolute percentage error, the DNN model improves the pricing power of call options by 63.74% and put options by 64.88% compared to the BS model. Additionally, from MSE, RMSE and MAE perspectives, as virtual value degree weakens and real value degree strengthens, out-of-sample pricing error of DNN model gradually increases indicating that virtual options generally have lower pricing errors than real options or value options do. However, from the MAPE perspective, as virtual value degree weakens and real value degree strengthens, the out-of-sample pricing error of the model gradually decreases, that is to say, the pricing error for real value options is generally lower than that for virtual or value ones. The selection of evaluation indices to assess the model does not have a uniform requirement, and the corresponding index can be chosen based on the actual needs of investment decision-making. From the perspective of MAPE, it is observed that as the remaining duration increases, the out-of-sample pricing error of SSE 50ETF options based on the DNN model gradually decreases. Particularly, in terms of pricing performance, flat options, real options, and deep real options show better results in medium-term and long-term scenarios. Therefore, this research not only enriches and enhances the application of existing non-parametric option pricing theory in China's option market but also provides valuable references for investors and risk managers with significant theoretical value and practical significance.
Of course, there are still some shortcomings in this study. For example, we can further consider implied volatility, SSE 50ETF volatility index iVX, conditional heteroscedasticity model, etc., in the selection of volatility. In terms of the input variables dimension of the deep neural network, we can further consider the influence of macroeconomic policy, investor sentiment, market liquidity and other factors on option pricing. The classical parametric option pricing models (such as the Heston model, double exponential jump model, variance gamma model) can be enhanced by introducing a deep learning method to build a hybrid option pricing model. Additionally, it is also an important topic worth exploring in the future how to mine financial text data and incorporate it into option pricing.

Key words: data-driven, deep learning, option pricing, Black-Scholes model, SSE 50ETF option

摘要： 近年来,以深度学习为代表的机器学习方法在金融领域中的应用越来越广泛。本文尝试将深度学习方法引入欧式期权定价研究中,构建了基于深度神经网络的非参数化期权定价模型(DNN模型),并利用上证50ETF期权交易数据进行了实证分析。研究发现:DNN模型的样本外定价误差显著低于经典的Black-Scholes模型(BS模型),并且从均方根误差来看,DNN模型在上证50ETF看涨期权上的定价精度较BS模型提升了76.97%;从平均绝对百分比误差来看,DNN模型在看涨期权上的定价精度较BS模型提升了63.74%,尤其在长期限和深度实值期权上表现出较高的定价精度。这些结果表明,基于深度学习的期权定价模型较BS模型在中国大陆期权市场上具有更高的定价精度,为投资者进行风险规避与衍生品定价提供了理论和实践依据。

关键词: 数据驱动, 深度学习, 期权定价, Black-Scholes模型, 上证50ETF期权