Option Hedging Practice
Spring 2021
1.
The management of HLG, a manufacturer of HVAC equipment, is concerned about potential increases in the
price of copper, a key component used in HVAC equipment. Management would like to establish a copper
purchase price for their upcoming copper needs in June. It is April. Copper is currently trading in the spot
market at $3.08. July copper futures are trading at $3.04 per pound. Historically spot copper prices have
traded $0.01 above futures three weeks before contract expiration.
Premiums for “at-the-money” July copper call and put options
Option Strike Price
Call Option Premium
$3.00
$0.15
$3.02
$0.14
$3.04
$0.13
$3.06
$0.12
$3.08
$0.11
Put Option Premium
$0.10
$0.11
$0.12
$0.14
$0.15
(a) To hedge, what type of option should management purchase?
Call Option, because they need to buy in the future.
(b) What intrinsic and time values are associated with the $3.04 option (option consistent with your choice in
part a)?
Intrinsic value = $0.00 ($3.04 (futures price) - $3.04 (call option strike price))
Time Value = $0.13 ($0.13 (premium) - $0.00 (intrinsic value)
(c) Management looks at the $3.04 and $3.06 options. What price ceilings are associated with these two
options?
$3.04 --> $3.04 (strike price) + $0.13 (premium) + $0.01 (expected basis) = $3.18 (expected price ceiling)
$3.06 --> $3.06 (strike price) + $0.12 (premium) + $0.01 (expected basis) = $3.19 (expected price ceiling)
Management decides to hedge its risk using the $3.06 option. On June 1, three weeks before the option’s
expiration, HLG’s production floor is ready to purchase copper in the local market. Copper futures have risen
to $3.15. HLG’s local copper supplier quotes a price of $3.16. The $3.06 option is trading at $0.14.
(d) If HLG management exercises their option, then offsets their futures position and purchases copper from
their local supplier what “realized price” would they face for copper (price inclusive of gains/losses in the
futures and options markets)?
$3.16 (spot) - [$3.15 (short futures) + $3.06 (long futures)] + $0.12 (option premium) = $3.19
(e) If HLG management offsets their option position and purchases, copper, from their local supplier what
“realized price” would they face for copper (price inclusive of gains/losses in the futures and options
markets)?
$3.16 (spot) - [$0.14 (option sale) - $0.12 (option purchase)] = $3.14
(f) If mill management had chosen to hedge using futures rather than options what realized price would they
face for the wheat (price inclusive of gains/losses in the futures and options markets)?
$3.16 (spot) - [$3.15 (short) - $3.04 (long)] = $3.05
S2 - (F2 - F1)
2.
The management of HLG, a manufacturer of HVAC equipment, is concerned about potential increases in the
price of copper, a key component used in HVAC equipment. Management would like to establish a copper
purchase price for their upcoming copper needs in June. It is April. Copper is currently trading in the spot
market at $3.08. July copper futures are trading at $3.04 per pound. Historically spot copper prices have
traded $0.01 above futures three weeks before contract expiration.
Premiums for “at-the-money” July copper call and put options
Option Strike Price
Call Option Premium
$3.00
$0.15
$3.02
$0.14
$3.04
$0.13
$3.06
$0.12
$3.08
$0.11
Put Option Premium
$0.10
$0.11
$0.12
$0.14
$0.15
(a) To hedge, what type of option should management purchase?
Call Option, because they need to buy in the future.
(b) What intrinsic and time values are associated with the $3.02 option (option consistent with your choice in
part a)?
Intrinsic value --> ($3.04 (futures price) - $3.02 (call option strike price)) = $0.02
Time Value --> ($0.14 (premium) - $0.02 (intrinsic value) = $0.12
(c) Management looks at the $3.02 and $3.06 options. What price ceilings are associated with these two
options?
$3.02--> $3.02 (strike price) + $0.14 (premium) + $0.01 (expected basis) = $3.17 (expected price ceiling)
$3.06 --> $3.06 (strike price) + $0.12 (premium) + $0.01 (expected basis) = $3.19 (expected price ceiling)
Management decides to hedge its risk using the $3.06 option. On June 1, three weeks before the option’s
expiration, HLG’s production floor is ready to purchase copper in the local market. Copper futures have fallen
to $2.85. HLG’s local copper supplier quotes a price of $2.87. The $3.06 option is trading at $0.04.
(d) Can HLG management exercise their option for a profit today? If management purchases copper from
their local supplier and lets the option expire what “realized price” would they face for copper (price
inclusive of gains/losses in the futures and options markets)?
$2.87(spot) + $0.12 (option premium) = $2.99
(e) If HLG management offsets their option position and purchases, copper, from their local supplier what
“realized price” would they face for copper (price inclusive of gains/losses in the futures and options
markets)?
$2.87 (spot) - [$0.04 (option sale) - $0.12 (option purchase)] = $2.95
(f) If HLG management had chosen to hedge using futures rather than options what realized price would they
face for the copper (price inclusive of gains/losses in the futures and options markets)?
$2.87 - ($2.85 - $3.04) = $3.06 (RHP)
3.
A soybean producer recently planted their crop and is concerned about a potential decline in the price of
soybeans between now and the time when the crop will be ready for sale in November. January soybean
futures are trading at 961 per bushel. The basis in November in the producer’s area has been 20 cents under
January futures. Initial and maintenance margins for soybean futures are $3,375 and $2,500 respectively.
“At-the-money” January soybean option premiums
Option Strike Price
Call Option Premium
940.0
35
950.0
30
960.0
25
970.0
21
980.0
17
Put Option Premium
15
19
24
30
37
(a) To hedge, what should the soybean producer do in the options market? Buy or sell? Put or call?
Buy a put option
(b) The producer is considering using an “out-of-the-money” option. Which options (strike prices) that fit this
description are available to the producer?
940-0, 950-0, 960-0
(c) Why might the producer choose to use an “out-of-the-money” option as opposed to an “in-the-money”
option?
Out-of-money is cheaper however if price falls the producer would be better of with In-the-money option.
they would have got with an in-the-money option.
The producer ends up choosing a $9.50 option. In November, the producer is ready to sell their soybeans in
the local market. The local elevator is buying soybeans for $10.50 per bushel. January futures are trading at
$10.62. The $9.50 option is trading at $0.05.
(d) What choices does the producer have in removing their option hedge? Does one make more sense than
another? Why?
Offset because there is no value in the other two options.
(e) If the producer removes the hedge using the most appropriate alternative (from those you discussed
above), what is their realized hedge price for their soybeans given that they hedged using options?
$10.50 + $0.05 - $0.19 = $10.36
(f) If the producer had hedged using futures rather than options what would their realized hedge have been?
$10.50 - ($10.62 - $9.61) = $9.49
(g) How much would each of the strategies cost the producer upfront (at the time when they placed the
hedging strategy)? Assume that the producer had 20,000 bushels (each futures contract represents 5,000
bushels)
Futures: 20,000 / 5,000 = 4 x 3,375 = 13,500
Options: 20,000 x 19 = 3,800
4.
A soybean producer recently planted their crop and is concerned about a potential decline in the price of
soybeans between now and the time when the crop will be ready for sale in November. January soybean
futures are trading at 961 per bushel. The basis in November in the producer’s area has been 20 cents under
January futures. Initial and maintenance margins for soybean futures are $3,375 and $2,500 respectively.
“At-the-money” January soybean option premiums
Option Strike Price
Call Option Premium
940.0
35
950.0
30
960.0
25
970.0
21
980.0
17
Put Option Premium
15
19
24
30
37
(a) To hedge, what should the soybean producer do in the options market? Buy or sell? Put or call?
Buy a put option
(b) The producer is considering using an “out-of-the-money” option. Which options (strike prices) that fit this
description are available to the producer?
940-0, 950-0, 960-0
(c) Why might the producer choose to use an “out-of-the-money” option as opposed to an “in-the-money”
option?
cheaper to buy out-of-money but if prices fall the producer should go with in-the-money.
The producer ends up choosing a $9.50 option. In November the producer is ready to sell their soybeans in
the local market. The local elevator is buying soybeans for $9.00 per bushel. January futures are trading at
$9.05. The 9.50 option is trading at $0.48.
(d) What choices does the producer have in removing their option hedge? Does one make more sense than
another? Why?
Offset their option because the other two have no value.
(e) If the producer removes the hedge using the most appropriate alternative (from those you discussed
above), what is their realized hedge price for their soybeans given that they hedged using options?
$9.00 + $0.48 - $0.19 = $9.29
(f) If the producer had hedged using futures rather than options what would their realized hedge have been?
$9.00 - ($9.05 - $9.61) = $9.56
(g) Based on your results in the previous problem (when the price increased) and your result for this problem
(when the price decreased) what inference can you make about the benefits of using futures and/or
options?
When prices fall using futures is more advantageous due to a locked in price. If prices rise the you can choose to exercise your
option...or not.
5.
Endeavor Refining, a New Mexico oil refining company, is concerned about a possible increase in crude oil
prices over the next six months due to a variety of factors including terrorism in the Middle East and domestic
political uncertainty. Because the plant manager is uncertain of the future and believes there is a chance that
oil prices could decrease, they decide to hedge their future oil purchases using options. Six-month-out oil
futures are trading at $56.13/barrel. Spot oil is trading at $56.83/barrel. Based on historic records the plant
manager believes that the basis in six months will be -0.10/barrel. Premiums for at-the-money options on sixmonth-out oil futures are shown below.
“At-the-money” oil option premiums for six-month-out options
Option Strike Price
Call Option Premium
$55.00
$5.08
$55.50
$4.80
$56.00
$4.53
$56.50
$4.27
$57.00
$4.02
Put Option Premium
$3.95
$4.18
$4.41
$4.64
$4.89
(a) What action should the plant manager take in the options market to hedge their upcoming oil purchase?
Buy a call option
(b) Which of the appropriate options (identified in part (a)) are “in-the-money?”
55.00 / 55.50 / 56.00
(c) Which of the options identified in part (b) will provide the “best protection” in terms of an expected
hedge price?
$56.00 ---> $56.00 (sp) + $-0.10 (expected basis) + $4.53 (premium) = $60.43 | $55.50 ---> $55.50 (sp) + $-0.10 (expected basis) +
$4.80 (premium) = $60.20 | $55.00 ---> $55.00 (sp) + $-0.10 (expected basis) + $5.08 (premium) = $59.98
(d) Why might the plant manager choose not to use the option (strike price) you identified above as having
the “best protection?”
It is expensive due to opportunity cost.
Assume the plant manager initiates the hedge using the cheapest in-the-money option available to them
(cheapest in terms of upfront costs). Six months pass and the plant manager is ready to remove their hedge.
Spot prices have moved to $65.00/barrel. Futures are trading at $65.10/barrel. The selected option is trading
at $9.05/barrel.
(e) Assume that the plant manager uses the most appropriate means of unwinding their hedge. What
method would they choose?
Offsetting
(f) What price did the plant manager have to pay, given that they chose to hedge with options?
$65.00 (spot) - [$9.05 (premium sale) - $4.53 (premium purchase) = $60.48
(g) How much did the plant manager gain or lose by hedging with their option?
$65.00 (spot) - $60.48 (hedge price) = $4.52 (gain)
6.
Endeavor Refining, a New Mexico oil refining company, is concerned about a possible increase in crude oil
prices over the next six months due to a variety of factors including terrorism in the Middle East and domestic
political uncertainty. Because the plant manager is uncertain of the future and believes there is a chance that
oil prices could decrease, they decide to hedge their future oil purchases using options. Six-month-out oil
futures are trading at $56.13/barrel. Spot oil is trading at $56.83/barrel. Based on historic records the plant
manager believes that the basis in six months will be -0.10/barrel. Premiums for at-the-money options on sixmonth-out oil futures are shown below.
“At-the-money” oil option premiums for six-month-out options
Option Strike Price
Call Option Premium
$55.00
$5.08
$55.50
$4.80
$56.00
$4.53
$56.50
$4.27
$57.00
$4.02
Put Option Premium
$3.95
$4.18
$4.41
$4.64
$4.89
(a) What action should the plant manager take in the options market to hedge their upcoming oil purchase?
Buy a call option
(b) Which of the appropriate options (identified in part (a)) are “in-the-money?”
56.00 / 55.50 / 57.00
(c) Which of the options identified in part (b) will provide the “best protection” in terms of an expected
hedge price?
$56.00 ---> $56.00 (sp) + $-0.10 (expected basis) + $4.53 (premium) = $60.43 | $55.50 ---> $55.50 (sp) + $-0.10 (expected basis) +
$4.80 (premium) = $60.20 | $55.00 ---> $55.00 (sp) + $-0.10 (expected basis) + $5.08 (premium) = $59.98
(d) Why might the plant manager choose not to use the option (strike price) you identified above as having
the “best protection?”
It is more expensive than the other two when considering upfront costs of their respective premium.
Assume the plant manager initiates the hedge using the cheapest in-the-money option available to them
(cheapest in terms of upfront costs). Six months pass and the plant manager is ready to remove their hedge.
Spot prices have moved to $55.00/barrel. Futures are trading at $55.10/barrel. The selected option is trading
at $0.05/barrel.
(e) Assume that the plant manager uses the most appropriate means of unwinding their hedge. What
method would they choose?
Offset to realize a $.05 gain in Time Value
(f) What price did the plant manager have to pay, given that they chose to hedge with options?
$55.00 (spot) - [$.05 (premium sale) - $4.53 (premium purchase) = $59.48
(g) How much did the plant manager gain or lose by hedging with their option?
$55.00 (spot) - $59.48 (hedge price) = -$4.48 (loss)
7.
Endeavor Refining, a New Mexico oil refining company, is concerned about a possible increase in crude oil
prices over the next six months due to a variety of factors including terrorism in the Middle East and domestic
political uncertainty. Because the plant manager is uncertain of the future and believes there is a chance that
oil prices could decrease, they decide to hedge their future oil purchases using options. Six-month-out oil
futures are trading at $56.13/barrel. Spot oil is trading at $56.83/barrel. Based on historic records the plant
manager believes that the basis in six months will be -0.10/barrel. Premiums for at- the-money options on sixmonth-out oil futures are shown below.
“At-the-money” oil option premiums for six-month-out options
Option Strike Price
Call Option Premium
$55.00
$5.08
$55.50
$4.80
$56.00
$4.53
$56.50
$4.27
$57.00
$4.02
Put Option Premium
$3.95
$4.18
$4.41
$4.64
$4.89
(a) What action should the plant manager take in the options market to hedge their upcoming oil purchase?
Buy a call option
(b) Which of the appropriate options (identified in part (a)) are “out-of-the-money?”
$56.50 - $57.00
(c) Assume the plant manager uses the option that is furthest out-of-the-money. What is their “expected
hedge ceiling?”
$57.00 + (-$.10) + $4.02 = $60.92
Six months pass and the plant manager is ready to remove their hedge. Spot prices have moved to
$65.00/barrel. Futures are trading at $65.10/barrel. The selected option is trading at $8.09/barrel.
(d) Assume that the plant manager uses the most appropriate means of unwinding their hedge. What
method would they choose?
Offset
(e) What price did the plant manager have to pay, given that they chose to hedge with options?
$65.00 (spot) - [$8.09 (premium sale) - $4.02 (premium purchase) = $60.93
(f) Compare your answer to part (d) to your answer from Problem 5, part (f). What do you learn from the
differences between the two answers?
Manager can use in or out of the money options but in the money will have lower prices if they move against the company.
8.
Endeavor Refining, a New Mexico oil refining company, is concerned about a possible increase in crude oil
prices over the next six months due to a variety of factors including terrorism in the Middle East and domestic
political uncertainty. Because the plant manager is uncertain of the future and believes there is a chance that
oil prices could decrease, they decide to hedge their future oil purchases using options. Six-month-out oil
futures are trading at $56.13/barrel. Spot oil is trading at $56.83/barrel. Based on historic records the plant
manager believes that the basis in six months will be -0.10/barrel. Premiums for at- the-money options on sixmonth-out oil futures are shown below.
“At-the-money” oil option premiums for six-month-out options
Option Strike Price
Call Option Premium
$55.00
$5.08
$55.50
$4.80
$56.00
$4.53
$56.50
$4.27
$57.00
$4.02
Put Option Premium
$3.95
$4.18
$4.41
$4.64
$4.89
(a) What action should the plant manager take in the options market to hedge their upcoming oil purchase?
Buy a call option
(b) Which of the appropriate options (identified in part (a)) are “out-of-the-money?”
$56.50 - $57.00
(c) Assume the plant manager uses the option that is furthest out-of-the-money. What is their “expected
hedge ceiling?”
$57.00 + (-$.10) + $4.02 = $60.92
Six months pass and the plant manager is ready to remove their hedge. Spot prices have moved to
$55.00/barrel. Futures are trading at $55.10/barrel. The selected option is trading at $0.09/barrel.
(d) Assume that the plant manager uses the most appropriate means of unwinding their hedge. What
method would they choose?
Offset
(e) What price did the plant manager have to pay, given that they chose to hedge with options?
$55.00 (spot) - [$.09 (premium sale) - $4.02 (premium purchase) = $58.93
(f) Compare your answer to part (e) to your answer from Problem 6, part (f). What do you learn from the
differences between the two answers?
Using out of the money allowed lower costs when the market moved with them.
9.
Summit Energy, a New Mexico oil production company, is concerned about a possible decrease in crude oil
prices over the next six months due to a variety of factors including trade tensions between the U.S. and
China. Because the company’s management is uncertain of the future and believes there is a chance that oil
prices could increase, they decide to hedge their future oil sales using options. Six-month-out oil futures are
trading at $56.13/barrel. Spot oil is trading at $56.83/barrel. Based on historic records the company’s
management believes that the basis in six months will be -0.10/barrel. Premiums for at- the-money options
on six-month-out oil futures are shown below.
“At-the-money” oil option premiums for six-month-out options
Option Strike Price
Call Option Premium
$55.00
$5.08
$55.50
$4.80
$56.00
$4.53
$56.50
$4.27
$57.00
$4.02
Put Option Premium
$3.95
$4.18
$4.41
$4.64
$4.89
(a) What action should the company manager take in the options market to hedge their upcoming oil sale?
Short the crude market with a put option purchase
(b) Which of the appropriate options (identified in part (a)) are “in-the-money?”
$56.50, $57.00
(c) Assume the plant manager uses an in-the-money option that is the closest to the current futures price.
What is their “expected hedge ceiling?”
$56.5 - $.1 - $4.64 = $51.76
Six months pass and the company manager is ready to remove their hedge. Spot prices have moved to
$55.00/barrel. Futures are trading at $55.10/barrel. The selected option is trading at $1.53/barrel.
(d) Assume that the company manager uses the most appropriate means of unwinding their hedge. What
method would they choose?
offset their option position as they are gaining .13 in time value. 56.5 -55.10 =-1.4 --> 1.53 - 1.40 = .13
(e) What price did the company manager receive for their oil, given that they chose to hedge with options?
$55 + $1.53 - $4.64 = $51.89
(f) How much did the company manager gain or lose by hedging with their option?
$51.89 - $55.00 = -$3.11 per/barrel or $1.53 - $4.64 = -$3.11
10. Summit Energy, a New Mexico oil production company, is concerned about a possible decrease in crude oil
prices over the next six months due to a variety of factors including trade tensions between the U.S. and
China. Because the company’s management is uncertain of the future and believes there is a chance that oil
prices could increase, they decide to hedge their future oil sales using options. Six-month-out oil futures are
trading at $56.13/barrel. Spot oil is trading at $56.83/barrel. Based on historic records the company’s
management believes that the basis in six months will be -0.10/barrel. Premiums for at- the-money options
on six-month-out oil futures are shown below.
“At-the-money” oil option premiums for six-month-out options
Option Strike Price
Call Option Premium
$55.00
$5.08
$55.50
$4.80
$56.00
$4.53
$56.50
$4.27
$57.00
$4.02
Put Option Premium
$3.95
$4.18
$4.41
$4.64
$4.89
(a) What action should the company manager take in the options market to hedge their upcoming oil sale?
Short the crude market with a put option purchase
(b) Which of the appropriate options (identified in part (a)) are “in-the-money?”
$56.50, $57.00
(c) Assume the plant manager uses an in-the-money option that is the closest to the current futures price.
What is their “expected hedge ceiling?”
$56.5 (sp) - $.1 (eb) - $4.64 (prem) = $51.76
Six months pass and the company manager is ready to remove their hedge. Spot prices have moved to
$65.00/barrel. Futures are trading at $65.10/barrel. The selected option is trading at $0.03/barrel.
(d) Assume that the company manager uses the most appropriate means of unwinding their hedge. What
method would they choose?
Offset option
(e) What price did the company manager receive for their oil, given that they chose to hedge with options?
$65 (spot) + $.03 (option) - $4.64 (premium) = $60.39
(f) If the company manager had hedged their future sales using futures, what price would they have received
for the oil?
$65.00 - ($65.10 - $56.13) = $56.03
(g) What can you conclude based on your answers for part (e) and part (f)?
Option trading takes advantage of the price movement we want vs being lock into a price using futures.