Consider a two-period binomial tree model with So = 4, u = 2, d = ], (i.e., S uS. and Sd = ds.) and take the one-period simple interest rate r = , so that p = = For n=0,1, 2, define Yn = {h=0 Sk to be the sum of the stock prices between times zero and n. Consider an Asian call option that expires at time two and has strike K = 4 (i.e., whose payoff at time two is (}Y 4)+.) This is like a European call, except the payoff of the option is based on the average stock price rather than the final stock price. Let vn(s, y) denote the price of this option at time n if Sn = s and Yn = y. In particular, V2(s, y) = (y 4)+. (a) Develop an algorithm for computing un recursively. In particular, write a formula for Vn in terms of Un+1. (b) Apply the recursive formula developed in (a) to compute vo(4,4), the price of the Asian option at time zero. (c) Provide a formula for On(s, y), the number of shares of stock that should be held by the replicating portfolio at time n if Sn =s and Yn = y