Question 2 (35 points] We are in a world with three periods (0, 1, and 2) and two assets, a risky non-dividend paying stock, and a money-market account (i.e., a risk-free bond). Assume that the price of the stock is now (period 0) So = 100 and between now and next period (period 1) it can go up by 20% or down by 20%. The same behaviour is exhibited also between periods 1 and 2. The risk-free rate of interest is r = 5%, between periods 0 and 1, and r2 = 3% between periods 1 and 2 (so that 1 invested in the bond at period 0, will be 1.05 at the end of period 1, and 1.05 x 1.03 at the end of period 2). (a) (10 points) Price a European Call and an American Call option on the stock with maturity T at the end of period 2 (i.e., T = 2) and strike price K = 90. For pricing the European Call, follow two approaches: (i) (5 points) using the risk-neutral probabilities, (ii) (5 points) by calculating the replicating portfolio at each node. (b) (10 points) Price a European Put and an American Put option on the stock with maturity at the end of period 2 and strike price K = 90. For pricing the European Put, follow two approaches: (i) (5 points) using the risk-neutral probabilities, (i) (5 points) by calculating the replicating portfolio at each node. (c) (10 points) Price a derivative on the stock with maturity at the end of period 2 and payoff at maturity of [K - Smin]t = max{K Smin, 0}, where K = 90, and ST = min min St. O