沪深300股指期权定价实证研究——基于BS、CEV、Heston模型的对比分析

An Empirical Study on the Pricing of CSI 300 Index Options—Based on BS, CEV, and Heston Models

摘要: 为研究沪深300股指期权定价，本文在对BS、CEV、Heston模型进行了理论分析和欧式期权定价解析式推导后，针对不同模型使用了不同的方法进行参数估计并实现了模型定价。最后本文借由对称平均绝对百分比误差(sMAPE)作为误差衡量指标，得出了实证结论：1) 三个模型对期权的估值整体呈现高估的态势，整体拟合优度CEV模型 > BS模型 > Heston模型；2) 从虚实期权角度来看，三个模型均对实值期权拟合效果更好，对虚值期权而言CEV模型拟合效果最好，对实值期权而言Heston模型拟合效果最好；3) 进一步探究发现，BS模型和CEV对短到期期限、低价值的期权拟合效果相对较好，Heston模型对低执行价、短到期期限、低价值的期权拟合效果较好。

Abstract: In order to study the CSI 300 stock index option pricing, after theoretical analysis of the BS, CEV, and Heston models and analytical derivation of European option pricing, different methods are used for parameter estimation and model pricing for different models. Finally, this paper uses the sym-metric mean absolute percentage error (sMAPE) as the error measurement index to draw the em-pirical conclusions: 1) The valuation of options by the three models is generally overestimated, and the overall goodness of fit: CEV model > BS model > Heston model; 2) From the perspective of out- of-the-money/real options, the three models are better for real options; The CEV model has the best fitting effect for out-of-the-money options, and the Heston model has the best fitting effect for real- valued options; 3) Further exploration found that the BS model and CEV have a relatively better fit-ting effect on short-expiration and low-value options, and the Heston model has a relatively better fitting effect on low-strike, short-expiration, and low-value options.