part b only,.

3. Consider a 3-period binomial model with u=2,d=21,r=41 and S0=8. Let Mn be the running maximum Mn=max0in(Si) (a) Find all the possible values for (M3,S3), that is {(M3(),S3()):}. Do not include repeat values. Find all the possible values for (M2,S2), that is {(M2(),S2()):}. (b) A lookback option, V, that makes a single payment V3=M3S3 at time 3 can be given a state representation in terms of (Mn,Sn). Find the backwards recursion relation and the terminal condition for this representation. (c) Use the terminal condition and the backward recursion relation to compute the arbitrage-free price of the lookback option in part (b)