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.
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