The power Asian option as an option where the payoff depends on the difference between power m of the geometric average price of the underlying asset during the life of the option and the power m of the strike price. The payoff from a power Asian call option is therefore
And, the payoff from power Asian put option is
Where m is any positive real number.
So, in case of Geometric power Asian option, the expectation and variance is given by
By putting this expectation and variance in Black’s formula (generalized version), we obtained power geometric Asian call and put option formulas as