基于插值修正的上证50ETF期权隐含高阶矩研究  

A Study on the Implied Higher-Moments of SSE 50ETF Options Based on Interpolation Correction

作　　者：王欣 王俊 叶五一[2] WANG Xin;WANG Jun;YE Wuyi(Huaan Securities Co.,Ltd,Hefei 230071,China;School of Management,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]华安证券股份有限公司,合肥230071 [2]中国科学技术大学管理学院,合肥230026

出　　处：《中国证券期货》2024年第6期21-31,48,共12页Securities & Futures of China

基　　金：国家自然科学基金面上项目(72371230);安徽省杰出青年基金项目(2208085J41)。

摘　　要：期权隐含高阶矩是衡量金融资产波动性和非对称性的关键指标。然而,真实市场中期权的执行价格具有离散性和有界性,直接应用理论方法基于市场离散期权数据计算的隐含高阶矩存在近似误差,影响指标可靠性。本文利用上证50ETF期权数据,采用无模型方法计算隐含波动率和隐含偏度指标,并通过“内插-外推”方法进行修正。研究结果表明:①未修正的隐含高阶矩通常被高估;②隐含波动率指数与上证50ETF收益之间存在显著的负相关性,这支持了市场存在杠杆效应和波动率反馈效应的理论;③隐含偏度指数与上证50ETF收益之间存在显著的正相关性,这可以理解为投资者更偏好右偏资产,而右偏资产价值倾向于被高估,从而导致负的收益;④在大多数时期,已实现波动率比隐含波动率低,这表明大多数投资者大部分时间倾向于规避风险,并且愿意为对冲风险支付费用。Option-implied higher-moments serve as key indicators of the volatility and asymmetry of financial assets.However,in real markets,the strike prices of options are discrete and bounded.This discreteness introduces approximation errors when theoretical methods are directly applied to calculate implied higher-moments,thereby affecting the reliability of these indicators.In this study,we employ a model-free method to calculate implied volatility and implied skewness indicators using the option data of the SSE 50ETF,and subsequently correct these indicators using the“interpolation-extrapolation”method.The findings of this study are as follows:①Uncorrected implied higher-moments tend to be overvalued;②There is a significant negative correlation between the implied volatility index and the returns of the SSE 50ETF,supporting the theory of a leverage effect and volatility feedback effect in the market;③A significant positive correlation exists between the implied skewness index and the returns of the SSE 50ETF,suggesting that investors prefer right-skewed assets,which tend to be overvalued and thus lead to negative returns;④Realized volatility is generally lower than implied volatility,indicating that most investors exhibit risk-averse behavior and are willing to pay for hedging risk.

关 键 词：期权隐含高阶矩 上证50ETF 已实现高阶矩 风险溢价 

分 类 号：O151.21[理学—数学] F832.5[理学—基础数学]