Exercise 1. A lookback option on a stock with price per share Sn that expires at time n -3 is a derivative security that pays out 0Sns3 at time n 3. Suppose the initial price per share of the stock is So 4 and that u-2,d- andso that p-, and q=2. (a) Determine the payout at expiration of the lookback option in all possible outcomes. That is, compute each of the following eight quantities: V(HHH), VS(HHT), VS(HTH), Vs(THH), Vs(HTT), Vs(THT), Vs(TTH) and Vs(TTT) (b) Use the backward recurrence relation of Theorem 1 below to complete the following. (i) Determine the value of the option Vn for all times n 0, 1,2 before expiration. (ii) Determine the -hedging process , 1, 2- Theorem 1. Consider an N-period binomial derivative pricing model with 0