Options where the payoff is based on the average price of the underlying asset, rather than the price of the underlying asset itself are known as "Asian" options. Asian options come in two broad categories, those based on a geometric average price, and those based on an arithmetic average price. (a) Consider the distribution of the product of a series of lognormally distributed random variables and a finite sum of a series of lognormal random variables. What implications does this have for the valuation of geometric and arithmetic average price Asian options in closed form