Pricing geometric Asian power options under mixed fractional Brownian motion environment

•Stock price is modeled with driving force as mixed fractional Brownian motion.•Closed form for the price of the geometric Asian option is derived.•Closed form for the price of the geometric Asian power option is derived.

It has been observed that the stock price process can be modeled with driving force as a mixed fractional Brownian motion with Hurst index H>34 whenever long-range dependence is possibly present. We obtain a closed form expression for the price of a geometric Asian option under the mixed fractional Brownian motion environment. We consider also Asian power options when the payoff function is a power function.