In the three-period model of Figure 1, let the interest rate be r = , and u = 2, and d = 1. f) Find the stock prices at different states (S(H), S(T), S2 (HH), S2 (HT), S (TH), S(TT), S(HHH), S3(THH), S3(HTH), S3(HHT), S3(TTH), S(HTT), S3 (THT), S(TTT)). ii) Find the risk-neutral probability p. iii) Determine the price at time zero of the American put that expires at time three and has intrinsic value gp(s) (5 s)+. iv) Determine the price at time zero of the American call that expires at time three and has intrinsic value gc(s) = (s-5)+.