2. (10 marks] CRR model: American call option. Assume the CRR model M= (BS) with the horizon date T = 2, the interest rate r = 0, and the stock price So = 45, SY = 49.5, S. = 40.5. Consider the American call option with the reward process (Sz, t) = (S4 - Kt) where the variable strike price satisfies Ko = 37, K1 = 35.5, K2 = 36.45. (a) Find the parameters u and d, compute the stock price at time t = 2, and find the risk-neutral probability P. (b) Compute the arbitrage price process for this option using the recursive relation- ship C = max {(s- Ki), (1 + r)-E (C+1F)} with the terminal condition C = (S. - K2)+. (c) Find the rational exercise time for the holder of this option. (d) Find the replicating strategy for the option up to the rational exercise time to and compute the initial wealth Vol). (e) Find the arbitrage price for the European call option with the payoff C (S- K2) at time T = 2 and compute the early exercise premium C8 - Co