Merton跳扩散模型下沪深300ETF期权定价的实证研究  

Empiricalstudy on the option pricing of CSI 300ETF based on Merton jump diffusion model

作　　者：王玉婵 单亮恩 WANG Yuchan;SHAN Liangen(School of Mathematics and Statistics,Nanjing University of Information Science&Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《齐鲁工业大学学报》2024年第6期74-80,共7页Journal of Qilu University of Technology

基　　金：江苏省高等学校自然科学研究项目(19KJB110018)。

摘　　要：沪深300ETF期权市场数据呈现“尖峰厚尾”的统计特征,与正态分布存在偏差,标的资产价格常常不是连续变化,在某一时间会存在“异常跳跃”,因此利用描述带“异常跳跃”现象的Merton跳扩散模型计算沪深300ETF期权价格。Merton跳扩散模型中隐含波动率参数、跳跃次数参数和跳跃幅度参数由历史数据估计,这些参数估计的质量直接影响期权价格的计算。因此首先利用异常值检验方法估计跳跃参数,然后基于Generalized Auto-regressive Conditional Heteroscedasticity(GARCH)模型估计隐含波动率,最后基于估计的模型参数和Merton跳扩散模型的定价公式计算期权价格。基于沪深300ETF期权数据的数值实验表明,结合GARCH参数估计的Merton跳扩散模型期权定价效果优于Merton跳扩散模型期权定价和结合GARCH参数估计的Black-Scholes模型期权定价。The CSI 300ETF option with the statistic characteristic of"peak and thick tail"does not obey a Gaussian distribution.The price of the underlying asset is often not continuous,and there will be some"abnormal jump"at certain moment.Therefore,the CSI 300ETF option price is calculated based on Merton jump diffusion model describing the"abnormal jump"phenomenon.The implied volatility and jump parameters in the Merton jump diffusion model are estimated from historical data,and these parameter estimations directly affects the calculation of numerical option prices.Therefore,in this paper,the jump parameters are estimated based on the judging outliers,and then the implied volatility is also estimated based on the Generalized Auto-regressive Conditional Heteroscedasticity(GARCH).Finally,based on the estimated model parameters,the option price is calculated with the help of the Merton jump diffusion model.Numerical experiments based on the empirical data of CSI 300ETF options show that the option prices can be calculated more effectively with the help of the Merton jump diffusion model combined with GARCH parameter estimation,compared with Merton jump diffusion model and Black-Scholes model combined with GARCH parameter estimation.

关 键 词：Merton跳扩散模型 GARCH模型 异常值检验 沪深300ETF 期权定价 

分 类 号：F224[经济管理—国民经济] F832.5