Question

Today is 1 May. Suppose you bought an American put option on October-maturing live cattle future contract with a strike price of 60 cents per pound. Each contract is for the delivery of 50000 pounds.

A).Please illustrate what happens if you exercise this option on 31 May when the October- maturing live cattle futures price is 50 cents per pound.

B).After exercising the put option, you decide to hold the underlying futures contract to the expiry and you closed out your future position on 31 October. Given that the October-maturing live cattle futures price is 45 cents per pound on 31 October, what is gain/loss on your future position. How much did spend on purchasing 50000 pounds of live cattle on 31 October ? (i.e. please ignore time value of money )

C).After taking the gain/loss of your futures position into account, what’s the effective price you’ve realised for 50000 pounds of live cattle on 31 October? Please detail all the steps in your answer. ( i.e.please ignore time value of money )

Answer 1

Strike Price, K = 60 cents per pound

Asset price on the day of exercise, S = 50 cents per pound

Quantity = Q = 50,000 pounds

Part (a)

If the option is exercised, your payoff = max (K - S, 0) x Q = max (60 - 50, 0) x 50,000 = 10 cents x 50,000 = $ 5,000

Part (b)

Future price on 31st May = F₀ = 50 cents per pound

Futures price on 31 October = F₁ = 45 cents per pound,

Gain/loss on your future position = (F₁ - F₀) x Q = (45 - 50) cents x 50,000 = - $ 2,500 i.e loss of $ 2,500

Amount spent on purchasing 50000 pounds of live cattle on 31 October = F₁ x Q = 45 cents per pound x 50,000 = $ 22,500

Part (c)

Amount spent = $ 22,500

Loss = $ 2,500

Total amount paid = $ 22,500 + 2,500 = $ 25,000

Q = 50,000

Price realized = Total amount paid / Q = $ 25,000 / 50,000 = $ 0.50 per pound = 50 cents per pound.