3. [20 marks] CRR model: American option. Consider the CRR model with T = 2 and So = 180, S 198, SI = 162. Assume that the interest rate r = 0. Consider the American call option with the reward process (St-Kt)+ where the variable strike price satisfies Ko = 148, K1 = 142, K2 = 145.8. (a) Find the parameters u and d, compute the stock price at time t = 2, and find the unique martingale measure P for the model. (b) Compute the arbitrage price process Ca for this option using the re- cursive relationship = max {(S. K.)+, (1 + r)-1 E (C+1 Fi)} with the terminal condition C = (S2 K2)+. (c) Find the rational exercise time to for the holder of the option. (d) Find the replicating strategy y for the option up to the rational exer- cise time ty and compute the initial wealth Vo(o). (e) Find the arbitrage price Co for the European call option with the payoff C2 = (S2 K2)+ at time T = 2 and compute the early exercise premium Co Co. 3. [20 marks] CRR model: American option. Consider the CRR model with T = 2 and So = 180, S 198, SI = 162. Assume that the interest rate r = 0. Consider the American call option with the reward process (St-Kt)+ where the variable strike price satisfies Ko = 148, K1 = 142, K2 = 145.8. (a) Find the parameters u and d, compute the stock price at time t = 2, and find the unique martingale measure P for the model. (b) Compute the arbitrage price process Ca for this option using the re- cursive relationship = max {(S. K.)+, (1 + r)-1 E (C+1 Fi)} with the terminal condition C = (S2 K2)+. (c) Find the rational exercise time to for the holder of the option. (d) Find the replicating strategy y for the option up to the rational exer- cise time ty and compute the initial wealth Vo(o). (e) Find the arbitrage price Co for the European call option with the payoff C2 = (S2 K2)+ at time T = 2 and compute the early exercise premium Co Co