关键词: 期权定价, Heston模型, 神经网络, 门控循环单元, CEEMDAN

Abstract: In recent years, China's options market has experienced rapid development and has been both regulated and supported by government. In the financial market, the price of an option is influenced by various factors, including the price of the underlying asset, the option's expiration date, volatility, interest rates, and so on. Therefore, accurate option pricing is essential for investors and market participants. Accurate option pricing can help investors develop reasonable investment strategies and risk management plans, and assist market participants in determining whether options are overvalued or undervalued, subsequently trading accordingly, reducing risk and losses, and enhancing market efficiency and liquidity.
The Black-Scholes (BS) option pricing model is one of the most widely used models in traditional option pricing. Its advantages include being simple and easy to understand, widely applicable, and providing the basic principles of option pricing. The model assumes that stock prices follow a log-normal distribution, which transforms the option pricing problem into a partial differential equation solving problems, and providing mathematical tools for option pricing. However, the model also has some drawbacks, such as the assumption of constant volatility, which cannot well reflect the changes in market volatility and the shape of the volatility curve, thus affecting the accuracy of option pricing. Some research attempts to relax some restrictive assumptions in the BS option pricing model and propose new pricing models, such as the Heston model and the Merton model, but these models still have some unreasonable assumptions, and the pricing results have significant deviations from market prices. Contrary to this, machine learning models do not rely on specific assumptions and pre-defined probability distributions, allowing them to better adapt to fluctuations in real-world market volatility and non-linear structures. Moreover, for complex options markets, the use of machine learning models can better address non-linear problems and high-dimensional data processing, thereby yielding more accurate pricing results.
Based on the above discussion, in order to more accurately price options, this paper proposes a Heston option pricing model that combines the ideas of “decomposition-reassembly-prediction-integration”. The model first utilizes the Heston pricing model for initial pricing and obtains pricing errors based on market prices. Then, the complex pricing errors are decomposed into a series of more regular fluctuations of Intrinsic Mode Functions (IMF) and residual use of the Completely Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and reconstructed into high-frequency sub-sequence, low-frequency sub-sequence, and trend term based on the calculated Approximate Entropy (AE) values of the IMF and residual. Finally, the high-frequency sub-sequence and low-frequency sub-sequence are modeled separately using Gated Recurrent Units (GRU), and the trend term is modeled using Auto Regressive Integrated Moving Average (ARIMA). The estimated values of the high-frequency sub-sequence, low-frequency sub-sequence, and trend term are added together to obtain the predicted values of the pricing errors. After using the predicted values of the pricing errors to modify the initial pricing results of the Heston model, the final option pricing results are obtained.
In order to evaluate the accuracy of the model proposed in this article, the authors conduct tests on the ChinaAMC China 50 ETF options, Huatai-PB CSI 300 ETF options, and Harvest SZSE SME-CHINEXT 300 ETF options, and compare the proposed model with several benchmark models. The experimental results demonstrate that the proposed model in this article achieves the highest direction accuracy (DA) of up to 84.13% and a minimum of 80.85% in all datasets, which is generally higher than the benchmark models. This indicates that the option pricing model proposed in this article has excellent pricing performance. Additionally, this also confirms the effectiveness of the “decomposition-reassembly-prediction-integration” strategy introduced in the Heston model in this article. This strategy not only improves the pricing accuracy of the model but also reduces its complexity.

Key words: option pricing, Heston model, neural network, gated recurrent unit, CEEMDAN