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.