Fractional Stochastic Volatility Pricing of European Option Based on Self-Adaptive Differential Evolution

Abstract

The option pricing model can predict the future trend of the financial market. In order to more accurately describe the changing process of the financial market, the Hurst index which can describe the characteristics of long-term memory is introduced into the traditional Heston model. Under the assumption that the underlying asset price follows fractional Brownian motion, the fractional stochastic volatility pricing of European option pricing model (Hurst-Heston model) is constructed, and the closed solution of the model is obtained according to the partial differential equation satisfied by the model. By analyzing the relationship between Hurst index and asset price, it is found that the movement process of asset price under the hypothesis of this model is more consistent with the real market change law, which verifies the rationality of the model. In the process of empirical analysis of SSE 50ETF put option data, Self-adaptive Differential Evolution algorithm is used to estimate parameters. The results showed that the error of Hurst-Heston model is smaller than other models, and the prediction error for consecutive trading days is similar. It showed that the pricing results of Hurst-Heston model are more accurate and stable.