Problem 1. This problem concerns the pricing of a European option in a two-period multiplicative binomial tree market. Suppose the present stock price is So = 50, the time interval is AT = 0.5 years, and the multiplicative factors are u = 1.2, d = 0.8 (so the stock price 0.5 years from now is either us, or dSo, and the stock price 1 year from now is either uSo, udSo, or d-So). Assume the risk-free rate is constant and is 4% per year. a) Find the no arbitrage price of a European put with strike 45 and maturity 1 year. S3(HHH) = uS. S2(HH) = uS. Si(H) = uso S3(HHT) = S3(HTH) S3(THH) = udo So S2(HT) = S2(TH) = udSo Si(T) = ds. S3(HTT) = S3(THT) = S3(TTH) = ud? So S2(TT) = dS. S3(TTT) = d So Fig. 1.2.1. General three-period model. Problem 1. This problem concerns the pricing of a European option in a two-period multiplicative binomial tree market. Suppose the present stock price is So = 50, the time interval is AT = 0.5 years, and the multiplicative factors are u = 1.2, d = 0.8 (so the stock price 0.5 years from now is either us, or dSo, and the stock price 1 year from now is either uSo, udSo, or d-So). Assume the risk-free rate is constant and is 4% per year. a) Find the no arbitrage price of a European put with strike 45 and maturity 1 year. S3(HHH) = uS. S2(HH) = uS. Si(H) = uso S3(HHT) = S3(HTH) S3(THH) = udo So S2(HT) = S2(TH) = udSo Si(T) = ds. S3(HTT) = S3(THT) = S3(TTH) = ud? So S2(TT) = dS. S3(TTT) = d So Fig. 1.2.1. General three-period model