Example 1.2.1. Consider the particular three-period model with So = 4, u = 2, and d = 1. We have the binomial "tree" of possible stock prices shown in Figure 1.2.2. Sz(HHH) = 32 S2(HH) = 16 S (H) = 8 S3(HHT) = S(HTH) S3(THH) = 8 So = 4 S2(HT) = S(TH) = 4 S(T) = 2 Sz(HTT) = S(THT) = S3(TTH) = 2 S2(TT) = 1 S(TTT) = .50 k= Problem 3. Repeat problem 2 for the European up-and-out call option with the strike 4 and up-and-out barrier 10, i.e. let us consider the settings of a three-period model of Example 1.2.1 on p. 9 with So = 4, u = 2, d = { and interest rate r = , so that = Q = }. For n = 0,1,2,3, define Mn = max Sk, the maximum of the stock price between times zero and n. Consider an up-and-out call option with the strike K = 4 and barrier B = 10, whose payoff at time T = 3 is given by max(ST - K,0), if MT SB, 0, if Mr >B Let un(s, m) be price of the option at time n if Sn = s and M. =m. In particular, V3(s, m) = max(s K,0)/(m B Let un(s, m) be price of the option at time n if Sn = s and M. =m. In particular, V3(s, m) = max(s K,0)/(m