. A futures price is currently 40. It is known that over each of the next two 3-

Question

. 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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Explanation / Answer

a) Using a european call, we get to avoid the decrease in price. The increase in price is 10% of 40 = $4.When discounted by 8% (risk free rate), the value is 4/power(1.08,0.5) = $ 3.85.

b) If the call were american, it would be exercising ealy if the price were such that the return would be greater than 8% per annum.

c) Using a european put, we get to avoid the increase in price. The decrease in price is 10% of 40 = $4.When discounted by 8% (risk free rate), the value is 4/power(1.08,0.5) = $ 3.85.

d) If the price decreases such that the loss from selling it would be equivalent to a negative return of -8%, the put can be excercised.

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