For Questions 1-2: Consider a binomial model. So = 4. In each period, the stock price doubles with a probability of 1/2 and halves with a probability of 1/2. The interest rate is r = 3. Suppose N = 2. Question 1 (20 points) (1) Find E[S2]; (2) Show that ( m )n) o is NOT a martingale under the (physical) probability P. Question 2 (20 points) A contract yields no payment at time t = 0, a payment at time t = 1 of $6 if the stock price decreases and of $0 otherwise, and a payment at time t = 2 of $36 if the stock price has jumped twice, of $18 if the stock price is equal to $4 and of $0 otherwise. What is the fair price of the contract at time t=0? For Questions 1-2: Consider a binomial model. So = 4. In each period, the stock price doubles with a probability of 1/2 and halves with a probability of 1/2. The interest rate is r = 3. Suppose N = 2. Question 1 (20 points) (1) Find E[S2]; (2) Show that ( m )n) o is NOT a martingale under the (physical) probability P. Question 2 (20 points) A contract yields no payment at time t = 0, a payment at time t = 1 of $6 if the stock price decreases and of $0 otherwise, and a payment at time t = 2 of $36 if the stock price has jumped twice, of $18 if the stock price is equal to $4 and of $0 otherwise. What is the fair price of the contract at time t=0