5. (35 points) Consider a multiperiod Binomial model in which T = 4 and there are two basic assets. One is riskless while the other one is a risky asset. The riskless asset's price at time t = 0 is $1 and the risk-free rate is 5% in each time period. There are two possibilities of the price movement for the risky asset; it can either move up to u = 125% or move down to d= 75% and S(0) = 100. Consider a European put option written on the risky asset with a strike price K = 100 and time to maturity T = 4. Assume the exercise time for this option is only at its maturity. (a) (5 points) Draw the binomial tree with the prices of the risky asset. (b) (4 points) What is the conditional risk neutral probability of up movement? (c) (5 points) What is the martingale measure of this model? (d) (5 points) What are the payoffs of the put option at time 4? (e) (4 points) What is the put price at time zero? (f) (12 points) What are the put prices at time 1, 2, and 3? 5. (35 points) Consider a multiperiod Binomial model in which T = 4 and there are two basic assets. One is riskless while the other one is a risky asset. The riskless asset's price at time t = 0 is $1 and the risk-free rate is 5% in each time period. There are two possibilities of the price movement for the risky asset; it can either move up to u = 125% or move down to d= 75% and S(0) = 100. Consider a European put option written on the risky asset with a strike price K = 100 and time to maturity T = 4. Assume the exercise time for this option is only at its maturity. (a) (5 points) Draw the binomial tree with the prices of the risky asset. (b) (4 points) What is the conditional risk neutral probability of up movement? (c) (5 points) What is the martingale measure of this model? (d) (5 points) What are the payoffs of the put option at time 4? (e) (4 points) What is the put price at time zero? (f) (12 points) What are the put prices at time 1, 2, and 3