3. (15 points) Consider an Asian call option with discounted payoff e'TTLg' K ]+ where K is the xed strike and T is the maturity. Here 5' is the arithmetic mean of the prices .9051), . . . , S(tm) with ti = iT/m,i = O, . . . , m. Assume S (t) follows a geometric Brownian motion. Suppose you are considering computing this payoff via stratifying the increments within a standard Brownian motion that is used to construct S(t) at discrete points in time t;- for i = 0, . . . , m. For example, stratify (oo, +00) into 711 disjoint intervals Ahi = 1, . . .,m st. {00, +00) = UiAi, and simulate a path with increments W(t) W(t_1) 6 Ai , i = 1, . . . ,m. You would then average the discounted payoffs across sample paths to come up with an estimator for the price of an option. Is this a good or bad idea? Explain your reasoning