Consider a two-period binomial tree model with So = 4, u = 2, d =, (i.e., S = uSo and st = d.So) and take the one-period simple interest rate r = ($1 of today becomes $ after one period.) so that p==. For n = 0,1,2, define Y = -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 u,(s, y) denote the price of this option at time n if Sn = s and Y = y. In particular, v(s, y) = (y - 4)+. (a) Develop an algorithm for computing un recursively. In particular, write a formula for Un 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 dn(s, y), the number of shares of stock that should be held by the replicating portfolio at time n if Sn = s and Y = y.