12. A futures price is currently 40. It is known that over each of the next two 3- month periods it will either rise by 10% or fall by 10%. The risk free interest rate is 8% per annum. (Consider using a 2-stage binomial tree for these questions.) a) What is the value of a 6-month European call option on the futures with a strike price of 40? (8 points) b) If the call were American, would it ever be worth exercising early? (2) c) What is the value of a 40 strike, 6-month European put option on the futures? (7) d) If the put were American, would it ever be worth exercising early? What would its value be? (3)