Question

You are concerned that faltering NAFTA renegotiations could jeopardize U.S. exports of cheese to Mexico. You think that current options prices are too cheap, since you believe prices will be more volatile than implied by the options prices. Using the information below on ATM options contracts for May 2018 Cash-Settled Cheese futures, assemble a straddle that will profit if you are correct that there is more volatility in the market than is currently priced into the options. • Current futures price: $1.546/lb • $1.550 call premium: $0.31 • $1.550 put premium: $0.35

a) Explain the positions you would take to speculate based on the belief above.

b) Find the price range(s) over which this belief would be profitable as well as your maximum profit and maximum loss.

c) Draw the payoff diagram for the straddle. For this payoff diagram, include both of the options positions as well as the combined position.

Answer 1

For this example:

C = Call premium, P = Put premium, S = Spot price on expiration, K = strike price

a) Explain the positions you would take to speculate based on the belief above.

We can create a straddle by:

• Buying the call option: Gain / (Loss) will be: max (S - K, 0) - C = max (S - 1.55, 0) - 0.31
• Buying the put option: Gain / (Loss) will be: max (K - S, 0) - P = max (1.55 - S, 0) - 0.35

b) Find the price range(s) over which this belief would be profitable as well as your maximum profit and maximum loss.

Resultant gain / (loss) = max (S - 1.55, 0) - 0.31 + max (1.55 - S, 0) - 0.35 = max (S - 1.55, 0) + max (1.55 - S, 0) - 0.66

Maximum profit is unlimited as the function goes up monotonically with S > $ 1.55

Maximum (loss) is when S = K = $ 1.55 and the quantum of loss = 0 + 0 - 0.66 = - $ 0.66

c) Draw the payoff diagram for the straddle. For this payoff diagram, include both of the options positions as well as the combined position.

Gain / (loss) matrix is:

S	Gain / (Loss)
	max (S - 1.55, 0) + max (1.55 - S, 0) - 0.66
-	0.89
0.50	0.39
1.00	(0.11)
1.50	(0.61)
2.00	(0.21)
2.50	0.29
3.00	0.79
3.50	1.29
4.00	1.79
4.50	2.29

And the diagram is: