. 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?

b) If the call were American, would it ever be worth exercising early?

c) What is the value of a 6-month European put option on the futures with a strike of 40?

d) If the put were American, would it ever be worth exercising early? What would its value be?

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