1. [5 marks] CRR model: American put option. Consider the CRR model with T = 2 and So = 100, S" = 120, ST = 90. Assume that the interest rate r = 0. Consider an American put option with reward process (Sc,t) = (Ki - S)' and variable strike price Ko = 105, K1 = 116, K2 = 111. (a) Find parameters u, d, the stock price at time T = 2, and a martingale measure P on (S2, F2). (b) Compute the price process Pa of this option using the recursive relationship Pa = max *{(K. S.)', (1+r) (524+ (1 ) ple) } K '1 with the terminal condition P = (K2-S2)'. (c) Find the holder's rational exercise time to (d) Find the replicating strategy for the option up to the exercise time to (e) Check whether the arbitrage price process (Pa; t = 0,1,2) is a martingale or a supermartingale under P with respect to the filtration F. - 1. [5 marks] CRR model: American put option. Consider the CRR model with T = 2 and So = 100, S" = 120, ST = 90. Assume that the interest rate r = 0. Consider an American put option with reward process (Sc,t) = (Ki - S)' and variable strike price Ko = 105, K1 = 116, K2 = 111. (a) Find parameters u, d, the stock price at time T = 2, and a martingale measure P on (S2, F2). (b) Compute the price process Pa of this option using the recursive relationship Pa = max *{(K. S.)', (1+r) (524+ (1 ) ple) } K '1 with the terminal condition P = (K2-S2)'. (c) Find the holder's rational exercise time to (d) Find the replicating strategy for the option up to the exercise time to (e) Check whether the arbitrage price process (Pa; t = 0,1,2) is a martingale or a supermartingale under P with respect to the filtration F