Consider a binomial model with 3 time periods. At time t = 0, the stock price is 40 dollars. After one time period, the stock can either go up to 80 dollars or it can go down to 20 dollars. Notice that in the upward jump, the stock price doubles, whereas in the downward jump, the stock price reduces to half the price before the jump. Assume this is true in each subsequent jump. At time t = 3, there are four possible values for the stock price: 320 dollars, 80 dollars, 20 dollars, and 5 dollars. Assume the interest rate r = 0.

Assume the same model for the stock price and interest rate is zero. 

(a). Consider a Call option with a strike price of 30 dollars that expires at time t = 3. Determine the value of this option at time t = 0. 

(b). Consider a Put option with the same strike price that expires at time t = 3. Use the put-call parity to determine the value of the option at time t = 0.