Consider a binomial model. S0 = 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 = 2 . Suppose N = 2.

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?