A stock has an initial price of S0 = 40. Sn denotes the price at time n, where we assume the binomial lattice model with parameters u = 1.22, d = 1.02, p = 0.55. Assume that the interest rate is r = 0.04.

(a) Compute the price of an option that has the following payoff at time T = 2:

C2 = max{S0, S1, S2} min{S0, S1, S2}.

(b) For the option in (a) suppose that at time n = 1 the stock price had gone "up": S1 = uS0. You decide to sell the option. Compute its price now (the price you can sell it for at time n = 1). Repeat for the case when at time n = 1 the stock price had gone "down": S1 = dS0.