基于局部波动率模型的上证50ETF期权定价研究  

Empirical analysis of Shanghai 50ETF options pricing based on local volatility model

作　　者：王西梅 赵延龙[1,2] 史若诗 包莹 WANG Ximei;ZHAO Yanlong;SHI Ruoshi;BAO Ying(LSC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100190,China;Risk Management Department,Indus trial and Commercial Bank of China,Beijing 100032,China)

机构地区：[1]中国科学院数学与系统科学研究院系统控制重点实验室,北京100190 [2]中国科学院大学数学科学学院,北京100190 [3]中国工商银行总行风险管理部,北京100032

出　　处：《系统工程理论与实践》2019年第10期2487-2501,共15页Systems Engineering-Theory & Practice

基　　金：国家重点研发计划项目(2018YFA0703800);国家自然科学基金(61622309)~~

摘　　要：局部波动率模型被广泛运用于风险管理、期权定价等领域,该模型不仅可以描述波动率微笑、期限结构等实际现象,同时能保证市场的完备性.研究局部波动率模型的核心目标是对隐含波动率进行建模.本文分别通过参数法和非参数法对隐含波动率建模,不仅保证了波动率曲面的无套利性,同时给出了非参数法求解局部波动率的显式表达式,从而消除了近似误差,得到较为光滑的波动率曲面.此外,本文基于局部波动率模型对我国上证50ETF指数期权的定价进行了实证研究,分别从样本内定价误差、样本外定价误差、套期保值效果三个方面分析比较了该模型的定价效果.实证结果显示:对样本内数据,非参数法拟合的定价结果优于参数方法;对样本外数据以及套期保值效果来说,参数法取得的效果较好.特别地,隐含波动率建模方法无论是对期权定价还是套期保值,效果均优于直接根据市场数据建模的结果,样本内定价误差可减少一半以上,均方误差可降低1~2个数量级.Local volatility model is widely used in the fields of risk management,options pricing,etc.The model can not only describe the"smile"and the term structure of volatility,but can also ensure the completeness of the market.The core goal of local volatility research is to calculate the implied volatility.In this paper,the implied volatility surfaces are built with both parametric and non-parametric methods to obtain smoother volatility surfaces.Parametric method can ensure the absence of arbitrage.Meanwhile,a closed form of solving the local volatility model with non-parametric method is proposed,which can eliminate the approximation error.In addition,the pricing of Shanghai 50 ETF option in China based on the local volatility model is studied by comparing effects of the models from aspects of in-the-sample,out-of-the sample and hedging pricing errors.The empirical results show that the non-parametric method is better than the parametric method for errors in-the-sample;the parametric method has better results for out-of-sample and hedging effects.Particularly,both the options pricing and hedging effects of the implied volatility modeling methods are better than un-modeled method in the aspects that the pricing errors can be decreased by more than half and the mean square error can be reduced by 1~2 orders of magnitude.

关 键 词：期权定价 隐含波动率 局部波动率模型 参数估计 

分 类 号：F830[经济管理—金融学]