[10 marks] CRR model: American call option. Consider the CRR model M = (B, S) with the horizon date T = 2, the interest rate r = 0, and the stock price SD = 45, S? = 49.5, Sf = 40.5. Consider the American call option with the reward process 9(8,, 1:) = (S, K,)+ where the variable strike price satises K0 = 37, K1 = 35.5, K2 = 36.45. (a) Find the parameters u and dkcompute the stock price at time t = 2, and nd the risk-neutral probability IE\". (b) Compute the arbitrage price process 0\" for this option using the recursive relationship C: = max {(815 KW\": (1 + 701 E(Cf+1 I19} with the terminal condition 05' = (32 K2)+. (c) Find the rational exercise time 73' for the holder of this option. ((1) Find the replicating strategy (,0 for the option up to the rational exercise time T5" and compute the initial wealth V0(