Empirical Research of the Pricing of Shanghai 50 ETF Options Based on Volatility and Fractional B-S Model

Abstract

By analyzing the closing price of Shanghai 50ETF options from 2017 to 2018, the authors find that the logarithmic return of 50ETF options has fractional characteristics. The fractional B-S model is used to analyze 50ETF option pricing. Firstly, the authors make R/S analysis of 50ETF option logarithmic return and get the Hurst index of the fractional B-S model. Secondly, the authors build the GARCH (1,1) model to characterize the volatility of 50ETF option’s yield and use the R software to get the historical volatility. Then the authors use fractional B-S model and the Matlab software to get the implied volatility. The authors make an empirical analysis on the pricing of 50ETF option based on the two kinds of volatility. The authors calculate the AMSE of results from the models with the market price, and compare them fully. It is found that the fractional B-S models based on the two kinds of volatility have good fitting effect on the pricing of 50ETF option, and the implicit volatility model has better fitting effect on the pricing of 50ETF option than the historical volatility model.