= [10 marks] CRR model: American call option. Assume the CRR model M = (B,S) with the horizon date T = 2, the interest rate r 0, and the stock price So 45, S 49.5, S 40.5. Consider the American call option with the reward process g(St, t) (St - Kt)+ where the variable strike price satisfies K₁ = 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 Ca for this option using the recursive relation- ship -1 Co = max {(S₁ − K₁)*, (1 + r)¯¹ Ep (C+1 | Ft)} with the terminal condition Cg = (S2 - K2)+. (c) Find the rational exercise time 7 for the holder of this option. 4 (d) Find the replicating strategy for the option up to the rational exercise time T and compute the initial wealth Vo(). (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.