Question

You are employed by the Treasurer’s office of a major airline company. Your assignment is to analyze possible hedging strategies using oil price futures.

• Today’s oil price is $55/barrel.

First, consider a European call option on oil price with a maturity of 1 year and a strike of $60. As in the class, the payoff does not count the premium of the option.

1. a) What is the payoff for the call option if the oil price stays at $55?

2. b) What is the payoff for the call option if the oil price increases to $65?

Next, consider a European put option on oil price with a maturity of 1 year and a strike of $60.

c) What is the payoff for the put option if the oil price stays at $55?

d) What is the payoff for the put option if the oil price increases to $65?

Lastly, we buy both the call and the put options as described above. This is called a straddle strategy.

5. e) What is the payoff of this strategy if the oil price stays at $55?

6. f) What is the payoff of this strategy if the oil price increases to $65?

7. g) What is the lowest payoff of this strategy? At what oil price is the lowest payoff obtained?

Answer 1

a. Since the strike price is more than the underlying's price, the payoff of the call option would be 0.

b. If it is $65, the payoff of the call would be = 65-60 = $5 (because underlying's price is more than strike)

c. If the price is $55 (less than strike), payoff of put option = 60-55 = $5.

d. If it increases to $65 (more than strike), payoff would be 0.

e. Using a and c, the payoff would be = 0+5 = $5.

f. Using b and d, the payoff would be = 0+5 = $5.

g. Since we are buying both, a call and a put and at the same strike price, we would always be profitable (positive payoff) except at the strike price i.e. $60. The payoff then would be 0 + 0 = $0.