1. Study carefully the following article:
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HW 4 Due on WED MAR 10 in class.
Study carefully the following article:
Crude oil protective puts by the State of Texas Texas, Other Governments, Trade in Commodities Futures
“Texas, along with other governments, is becoming a big-time player in the commodities market.
But it’s not because they’ve become bored with their own lottery operations. Quite the contrary;
their goal is not to take risks, but to reduce them. If the word hedging does not yet appear in the
codification of government accounting standards, you can be certain that it will soon.
Texas uses commodity options to protect its tax revenues from sudden drops in the price of oil.
Texas expects to generate $500 million from its oil severance tax. For every barrel of the "black
gold" produced in the state, the Treasury receives 4.6 percent of the sales price. A sharp drop in
price, such as in 1986 when it nose-dived from almost $25.82 to 11.36, can play havoc with the
state’s budget.
To lock in a set price, the state is experimenting with oil options. Here’s how they work.
The State purchases put options on crude oil. Each option permits it to sell (or “put”) a
thousand (1,000) barrels of oil at an established (exercise) price to the party that sold the option
on a specified (exercise) date. If on the exercise date the market price of crude oil is below the
established price, then the option has value: the intrinsic value - the difference between the
established exercise price and the market price. The state either exercises the option or sells it in
the open market, thus making a “profit” and covering the cost of the oil itself. The greater the
decline in market price, the greater the gain to the state from the put.. If, however, the oil
market price on the specified date is above the established exercise price, then the option has no
value and the state will allow it to expire worthless. Its loss is limited to the amount that it paid to
acquire the option (the “premium” cost).
The Texas Treasury can be viewed as the de facto owner of 4.6 percent (the severance tax rate) of all the oil produced in the state. Therefore, for each 1,000 barrels of oil that it wants to protect against a decline in revenue, it must buy puts on 46 barrels.
Suppose that on June 1, the State buys puts on 100,000 barrels of oil, thereby protecting 2,173,913 barrels (100,000 divided by 4.6 percent). Since put contracts are written in units of 1,000 barrels, the State would be required to buy 100 contracts. Assume that on the date the puts are purchased the prevailing market price is S = $21 per barrel and that this is the price that the state wants to lock in for purposes of severance tax collection three months hence. Therefore it buys puts with X = $21 as the strike price and T = October 1 as the expiration date. The cost of each contract might be approximately $1,100 including commissions---$110,000 for the 100 contracts.

2. Assume that today, Texas crude oil is selling for
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If, on the expiration date, the market value of oil has fallen to ST = $18 per barrel, then the market value of each contract can be expected to approximate $3,000 [($21-$18)(1,000)] barrels]-or $300,000 for the 100 contracts. This amount will be just sufficient to offset the loss on the severance tax revenue from the $3 per barrel price drop (2,173,913 barrels times $3 per barrel times the tax rate of 4.6 percent). The state will sell the options for the $300,000 and its net loss on the entire transaction will be $110,000, the cost of the options.
If on the expiration date, the price of oil is $21 or more, then the options will have no value and the state will be out the $110,000 that it paid for them. However, the state will still reap the benefits from the increased tax revenue owing to the rise in oil prices, and this additional revenue may be sufficient to offset all or at least a part of the option cost.”
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Assume that today, Texas crude oil is selling for
St = $87.18/barrel (bbl).
Also assume that today, calls and puts on Texas crude for Jan11 Expiration are traded for the following prices (premiums) per barrel:
K calls puts
$85.00/bbl $2.60/bbl $1.18/bbl
$85.50/bbl $2.30/bbl $1.38/bbl
$86.00/bbl $2.03/bbl $1.65/bbl
$86.50/bbl $1.79/bbl $1.86/bbl
$87.00/bbl $1.58/bbl $2.13/bbl
$87.50/bbl $1.38/bbl $2.43/bbl
$88.50/bbl $0.46/bbl $2.99/bbl
The State of Texas expects the price of Texas crude to be between $86/bbl and $88/bbl in Jan11, but wishes to hedge its severance tax revenue in case the crude’s price falls below $85. Based on production data from the last 5 years, the Texas Railroad Commission figures that by the options’ Jan11 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 today and the expiration date on Jan11.

3. An important assumption
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For solving problems 1,2,3 and 4 you must make:
An important assumption
All the 152,000,000 barrels are sold on the Jan11
options’ expiration day.
Moreover, you must use the following:
Important Hint:
For Q1 and Q3 do not account for the underlying
crude current price in the ICF. The cash flow
associated with the crude oil sale should appear in
the table only at Jan11 expiration.
Q1. The State buys the $85.50, Jan11 puts.
Use a table of cash flows per barrel to describe the initial cash flow and the terminal cash flow in Jan11 from this long put strategy.
Q2. Graph the P/L profile of the State from the strategy in Q1, using all possible prices per barrel at expiration.
Q3. The State opens the following collar :
[Long the K1=$85.50, Jan11 puts and Short the K2= $87.50 Jan11 calls] Describe the initial cash flows and the terminal cash flows at Jan11 from the collar using a table format. Use prices per barrel.
Q4. Graph the P/L profile of the State from the strategy in Q4, using all possible prices per barrel at expiration.

4. Q5. For Q5 and Q6 use the table below. p4 of 4
5.1 Your broker calls you and tells you that the MAR, call, which is listed for
2.63/share, is actually selling now for 1.60/share. The option is an American call.
Explain how to make immediate arbitrage profit, without having to wait till the
option’s expiration.
5.2 Your broker calls you again and informs you that actually, this call is European.
Explain how you can still, make arbitrage profit, although this time, the strategy requires of you to wait until the option’s expiration.
Q6. Your broker calls yet, once more, suggesting that you open a Box spread based
on the APR, 30 and the APR, 35 options prices.
6.1 Use a table of cash flows to verify that this strategy guarantees you $5 at the options expiration.
6.2 Calculate the risk-free rate you earn from this strategy.
6.3 Compare the risk-free rate you calculated in 6.2 with the market risk-free rate,
given below the table. If they are not equal, explain how to open an arbitrage profit
making strategy.
6.4 Analyze the P/L at expiration of strategy you suggest in 6.3 and show that it really is an arbitrage strategy.
Call
Put S K
MAR
APR
JUL
29.50
25.00
4.88
5.30
7.00
.44
1.00
2.08
27.50
2.63
3.63 -
1.94 30
1.56
2.44
2.00
3.00
32.50
.53
1.83
3.50
4.50 35
.31
.81
2.19
5.75
6.25
7.38
37.50
.50
9.00 40
.08
1.25
11.13
11.25
11.50
Expiration dates: March 16(18 days); April 20 (53 days) and July 20 (144 days).
The respective annual risk-free rates are: 5%, 4.85% and 4.52%.