Pricing Asian Power Options Under Mixed Fractional Brownian Motion Environment With Jumps

Options used for hedging can well hedge against risks.But the financial market in China started late,and is still in the initial stage of development at present.Options are scarce and there is a certain gap with the international market,which cannot meet the needs of hedging specific portfolios.Therefore completing the options market to increase the vitality of Chinese economic development is the top priorities in developing Chinese financial market.Asian power options,as a recombination of Asian options and power options,combine the characteristics of two options,which enriches the financial market,and has a certain practicability.Most of the current researches on Asian power options are assumed that the stock price changes continuously,but in the actual financial market,stock prices will jump intermittently due to certain events.Considering this characteristic of stock price,this paper introduces jump-diffusion process into the mixed fractional Brownian motion model to describe the dynamic change of stock price.Assuming that the price of the underlying asset follows the mixed fractional Brownian motion with jumps,according to the risk-free pricing principle and mixed fraction jump-diffusion Ito formula,this paper deduces the pricing formulas of the call options of geometric Asian power options with fixed strike price,in the case of without paying transaction cost and paying transaction cost when trading stocks respectively.Numerical experiments identify and test the jump of stock price,verify the rationality of its motion pattern description and the correctness of the mixed fractional Brownian motion with jumps model in pricing Asian power options,ex?plore the influence of jump intensity λ and power index n on the value of geometric Asian power options,and illustrate the positive significance of introducing Asian power options in developing Chinese options market.