= Consider pricing this option using the binomial model. Let the current price of stock in Hindsight Inc. be So = 108 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 triples u = 3, or falls to a third d= i = } (a) Calculate the risk neutral probability of an uptick p. (b) An important property of lookback options not shared by vanilla calls and puts is that they are path dependent. That is, their payoffs depend not only on the final stock price but on how the price moved over the life of the option. Show that this option is path dependent, that is, find two price paths that end at the same price. Draw the stock price tree. Note that there are 2" 8 ible price pat in contrast to the n+1 = 4 different final prices, so this should be drawn as a fully branching tree where the number of nodes doubles with each step. The option payoffs are shown at each of the final nodes. Using backward induction, calculate the initial price of this option. (d) = Consider pricing this option using the binomial model. Let the current price of stock in Hindsight Inc. be So = 108 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 triples u = 3, or falls to a third d= i = } (a) Calculate the risk neutral probability of an uptick p. (b) An important property of lookback options not shared by vanilla calls and puts is that they are path dependent. That is, their payoffs depend not only on the final stock price but on how the price moved over the life of the option. Show that this option is path dependent, that is, find two price paths that end at the same price. Draw the stock price tree. Note that there are 2" 8 ible price pat in contrast to the n+1 = 4 different final prices, so this should be drawn as a fully branching tree where the number of nodes doubles with each step. The option payoffs are shown at each of the final nodes. Using backward induction, calculate the initial price of this option. (d)