3. Consider a derivative that gives the buyer an option to receive the average of the past stock price values (including today's price) by paying. 100 dollars. The stock currently trades at S(0) = 100. Suppose this is a four-month option, and we compute its price using two periods only, each of length equal to two months. Your model is a two period binomial tree with u = 1.01 and d = 1/u. We use a continuously compounded annual interest rate r = 0.01. The averages are computed using the stock prices at the beginning of each period, S(0), S(T/2) and S(T). - (i) Compute the no-arbitrage price of the European version of the deriva- tive. - (ii) Compute the no-arbitrage price of the American version of the derivative.