- 2. [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, Su 49.5, Sd=40.5. Consider the American call option with the reward process g(St,t) (StKt) where the variable strike price satisfies Ko = 37, K₁ = 35.5, K2 = 36.45. - (a) Find the parameters u and d, compute the stock price at time t risk-neutral probability P. = = 2, and find the (b) Compute the arbitrage price process Ca for this option using the recursive relation- ship C = max ax {(St − K₁)+, (1+r)¯¹ Ep(Ci 4+1 | Ft)} with the terminal condition C = (S2 - K2)+. (c) Find the rational exercise time for the holder of this option. (d) Find the replicating strategy for the option up to the rational exercise time T and compute the initial wealth Vo(y). (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.