You are employed by the Treasurer’s office of United Airlines. Your assignment is to help the Treasurer analyze possible hedging strategies for the firm’s exposure to fluctuations in the price of oil. You have estimated that, without any hedging, the United’s profit will drop $50 million for $1 increase in the price of oil. Furthermore, you estimate that the profit would be 0 if the price of oil is $100.

Assume that you have the following 1-year European quotes for options on crude oil, quoted per barrel of oil, from an investment bank.

Strike price                  Call option price           Put option price

$50.00 / barrel                  $7.47                                   $1.97

$55.00 / barrel                  $4.64                                   $4.10

$60.00 / barrel                  $2.69                                   $7.10

$65.00 / barrel                  $1.46                                   $10.82

$70.00 / barrel                  $0.76                                   $15.07

(a) What is the least cost single option position they should take (which option, how many options, buy or sell) to guarantee profit of at least $2 billion, before the cost of the hedging program?

(b) What is the cost of the hedging program in (a)?

(c) What option positions should they take (which options, how many options, buy or sell) to eliminate all oil price risk and secure a profit flow of $2 billion, before the cost of the hedging program?

(d) What is the cost of the hedging program in (c)? Is it higher or lower than the initial hedging program calculated in part (b)? Why?