Consider a two-period binomial tree where the initial stock price is S0 = 50, and u = 1.26 and d = 0.78. Using obvious notation, we call the two nodes after one period the unode and the dnode, and the label the four nodes after two periods as the uu, ud, du, and ddnodes. Thus, e.g., the udnode is reached after first multipying S0 by u and then by d. In the following questions, you have to determine the numerical value of the payoff of certain options with no early exercise (that expire at the end of the second period) at each of the four nodes after two periods. It suffices to give the answer, and only the numerical answer matter

(a) An arithmetic average strike Asian call option. Each node is at the end of a path consisting of three nodes, and the arithmetic average is taken over the stock prices at the three nodes. 2 Answer: The payoffs are as follows:

at the uunode:

at the udnode:

at the dunode:

at the ddnode:

(b) An up-and-out barrier call option, with barrier B = 65 and strike price K = 45.

Answer: The payoffs are as follows:

at the uunode:

at the udnode:

at the dunode:

at the ddnode:

(c) A standard lookback put option. Answer: The payoffs are as follows:

at the uunode:

at the udnode:

at the dunode:

at the ddnode: