1. Due in on Tuesday, February 11, in class.
Study carefully the page entitled “Crude oil protective puts by The State of Texas.”
In addition, you are given the following information:
Today is a day in February. Texas crude oil is selling today for St = $31.18/bbl.
Today, calls and puts on Texas crude for MAY Expiration are traded for the following prices per barrel:
X calls puts
$30.00/bbl $2.60/bbl $1.18/bbl
$30.50/bbl $2.30/bbl $1.38/bbl
$31.00/bbl $2.03/bbl $1.65/bbl
$31.50/bbl $1.79/bbl $1.86/bbl
$32.00/bbl $1.58/bbl $2.13/bbl
$32.50/bbl $1.38/bbl $2.43/bbl
$33.50/bbl $0.46/bbl $2.99/bbl
The State of Texas expects the price of Texas crude to be between $31/bbl and $32/bbl in May, but wishes to hedge its severance tax revenue in case the crude’s price falls below $30. Based on production data from the last 5 years, the Texas Railroad Commission figures that by the options’ May expiration date, it needs to protect the 4.6% severance tax revenue from the sale of 152,000,000 barrels of oil that are expected to be produced and sold between now (February) and the expiration date on May.
Hint: For Q1, Q3 and Q5 do not account for the underlying crude current price in the I.C.F. The cash flow associated with the crude sale at expiration should be added to the table only at May expiration.
Q1. The state buys the $30.50, May puts. Describe the initial cash flow and the terminal cash flow in May from the protective put strategy. Show the results in a table format for $ per barrel, as well as in total $s, assuming that the actual number of barrels produced and sold was 152,000,000. Recall, the tax is 4.6% and one option is for 1,000 barrels.
Q2. Graph the P/L profile of the state from the strategy in Q1, using the per barrel prices at expiration.
Q3. Instead of the protective puts of Q1., the state uses a collar, buying the $30.50 May puts and selling the $32.50 May calls to finance the puts. Describe the initial cash flow and the terminal cash flow in May from the collar. Show the results in a table format for $ per barrel, as well as in total $s, assuming that the actual number of barrels produced and sold was 152,000,000.Recall. The tax is 4.6% and an option is for 1,000 barrels.
Q4. Graph the P/L profile of the state from the strategy in Q3, using the per barrel prices at expiration.

2. Q5. As an independent consultant to the State, your estimate of the probability of the crude price to climb above $32.50 by the end of May is 10%, while the probability that it will surpass $33.50 is only 1%. Thus, you suggest that the State opens the following strategy:
Long the $30.50 put and sell three, $33.50 calls.
Show the P/L profile in May expiration in a table format for $ per barrel, as well as in total $s, assuming that the actual number of barrels produced and sold was 152,000,000. Recall, the tax is 4.6% and and option is for 1,000 barrels.
Q6. Graph the P/L profile of the state from the strategy in Q5, using the per barrel prices at expiration.
Q7. Indicate in which crude oil price ranges each of the above the three strategies is better than the others.