The geometric average of the lognormally distributed random variables is a lognormal. And, Kemna and Vorst showed the expectation and variance of geometric average and derived the European style call and put options formula. The expectation and variance of geometric average is given by

Where n(a,b) represents a normal distribution with mean a and variance b. Hence, by putting

and

in Black’s formula (generalized version), we obtained geometric Asian call and put option formulas as