2. (40) Consider a special type of lookback option Whose payoff at maturity is given by the difference between the maximum and minimum stock prices attained over the life of the option. LT = max St min St te[0,T] te[0,T] Consider pricing this option using the binomial model. Let the current price of stock in Hindsight Inc. be $0 = 216 and consider an option maturing in n = T = 3 periods, so that At = 1 per period. Suppose for the sake of simplicity that the risk free rate is r = 0, and that each period the stock price either doubles 'u = 2, or falls by half d = i = % (c) (15) Draw the stock price tree. Note that there are 2" = 8 possible price paths, in contrast to the n+1 = 4 different final prices