Consider a two-period binomial tree model with S0 = 4, u = 2, d = 12 , (i.e., Su1 = uS0and Sd1 = dS0) and take the one-period simple interest rate r = 14 , so that p = q = 12 .For n = 0, 1, 2, define Yn = nk=0 Sk to be the sum of the stock prices between times zeroand n. Consider an Asian call option that expires at time two and has strike K = 4 (i.e.,whose payoff at time two is (13 Y2 4)+.) This is like a European call, except the payoffof the option is based on the average stock price rather than the final stock price. Letvn(s, y) denote the price of this option at time n if Sn = s and Yn = y. In particular,v2(s, y) = ( 13 y 4)+.(a) Develop an algorithm for computing vn recursively. In particular, write a formula forvn in terms of vn+1.(b) Apply the recursive formula developed in (a) to compute v0(4, 4), the price of theAsian option at time zero.(c) Provide a formula for n(s, y), the number of shares of stock that should be held bythe replicating portfolio at time n if Sn = s and Yn = y.