The exchange option is a contract that gives the holder the right to exchange one unit of asset B for k units of asset A. Hence the payoff of the European exchange call option can be written as Cexchange = max {0, kS^(T) - SB(T)} 0 =s"(T) max {o , desain *-1} SB(T) The way to price these exchange options is by modeling the dynamics of the ratio of the two prices instead of the dynamics of each stock price. For example, consider a 1-period binomial tree. The initial ratio is given by Next period the ratio can go up to ux tree be given by or down to dx , Let the data of this one-period S = 100 Sb = 125 u= 2 d=0.5 Assume no dividend payments for stock A or B. Assume no dividend payments for stock A or B. (i) (20 points) Compute a replicating portfolio for the 1-period European exchange call option that invests in stock A and stock B. How many shares of stock A and stock B do you want to buy? Use this replicating portfolio to determine the price of the call as a function of k. (ii) (5 points) Show that the American exchange call has exactly the same price as the European exchange call regardless of the value of k. (iii) (5 points) Use the price of the exchange option to find the price of the call that pays the maximum of the two stocks, that is, the one with a final payoff: max {SA(T), S (T)}