基于“分解-重组-预测-集成”模式的Heston期权定价模型  

Heston Options Pricing Model Based on the Principle of“Decomposition-Reassembly-Prediction-Integration”

作　　者：姚远[1] 张朝阳 赵阳 李艳 李方方 黄蕾 YAO Yuan;ZHANG Zhaoyang;ZHAO Yang;LI Yan;LI Fangfang;HUANG Lei(Institute for Management Science and Engineering,Henan University,Kaifeng 475004,China)

机构地区：[1]河南大学管理科学与工程研究所,河南开封475004

出　　处：《运筹与管理》2024年第2期172-178,共7页Operations Research and Management Science

基　　金：国家社会科学基金资助项目(17BJY194);河南省高等学校哲学社会科学基础研究重大项目(2021-JCZD-01);河南大学哲学社会科学重大项目培育计划(2019ZDXM016)。

摘　　要：精准合理地期权定价对于改善市场流动性、优化投资者结构、稳定金融市场拥有重要意义。本文提出了一种结合“分解-重组-预测-集成”思想的Heston期权定价模型,该模型利用Heston模型进行初始定价,通过自适应噪声完全集合经验模态分解(CEEMDAN)对定价误差进行分解与重构,获得高频项、低频项及趋势项,然后使用门控循环单元(GRU)估计高频项及低频项,使用差分整合移动平均自回归(ARIMA)估计趋势项,所有估计值集成汇总得到定价误差估计值,最后使用定价误差估计值对Heston模型的初始定价结果进行修正后获得最终定价结果。使用华夏上证50ETF、华泰柏瑞沪深300ETF和嘉实沪深300ETF期权数据验证模型,实证结果显示,在模型结构更加简单的基础上,本文提出模型的精度普遍优于基准模型。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-dime

关 键 词：期权定价 Heston模型 神经网络 门控循环单元 CEEMDAN 

分 类 号：F830.9[经济管理—金融学]