1. [10 marks] CRR model: American call option. Assume the CRR model with T = 2, the stock price So = 45, S = 49.5, SI = 40.5 and the interest rate r = -0.05. Consider the American call option with the reward process g(St, t) = (St Kt)+ for t = 0,1,2 where the random strike price satisfies Ko 40, K1(w) = 35.5 for WE {W1,W2}, K1(w) = 38.5 for w e{w3, wa} and K2 = 36.45. (a) Find the parameters u and d, compute the stock price at time t = 2 and find the unique martingale measure P. (b) Compute the price process C for this option using the recursive relationship Co = max {{S: K;), (1+r)-+E;(C+1 | F:)} with the terminal condition C9 = (S2 K2)+. (c) Find the rational exercise time for the holder of this option. (d) Find the issuer's replicating strategy for the option up to the rational exer- cise time to and show that the wealth of the replicating strategy matches the price computed in part (b). (e) Compute the profit of the issuer at time T if the holder decides to exercise the option at time T. 1. [10 marks] CRR model: American call option. Assume the CRR model with T = 2, the stock price So = 45, S = 49.5, SI = 40.5 and the interest rate r = -0.05. Consider the American call option with the reward process g(St, t) = (St Kt)+ for t = 0,1,2 where the random strike price satisfies Ko 40, K1(w) = 35.5 for WE {W1,W2}, K1(w) = 38.5 for w e{w3, wa} and K2 = 36.45. (a) Find the parameters u and d, compute the stock price at time t = 2 and find the unique martingale measure P. (b) Compute the price process C for this option using the recursive relationship Co = max {{S: K;), (1+r)-+E;(C+1 | F:)} with the terminal condition C9 = (S2 K2)+. (c) Find the rational exercise time for the holder of this option. (d) Find the issuer's replicating strategy for the option up to the rational exer- cise time to and show that the wealth of the replicating strategy matches the price computed in part (b). (e) Compute the profit of the issuer at time T if the holder decides to exercise the option at time T