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Options, Futures, and Other Derivatives

John C. Hull

Chapter 2

Futures markets and central counterparties - all with Video Answers

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Chapter Questions

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Problem 1

Distinguish between the terms open interest and trading volume.

Nick Johnson
Nick Johnson
Numerade Educator

Problem 2

What is the difference between a local and a futures commission merchant?

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Problem 3

Suppose that you enter into a short futures contract to sell July silver for $$\$ 17.20$$ per ounce. The size of the contract is 5,000 ounces. The initial margin is $$\$ 4,000$$, and the maintenance margin is $$\$ 3,000$$. What change in the futures price will lead to a margin call? What happens if you do not meet the margin call?

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Problem 4

Suppose that in September 2018 a company takes a long position in a contract on May 2019 crude oil futures. It closes out its position in March 2019. The futures price (per barrel) is $$\$ 48.30$$ when it enters into the contract, $$\$ 50.50$$ when it closes out its position, and $$\$ 49.10$$ at the end of December 2018. One contract is for the delivery of 1,000 barrels. What is the company's total profit? When is it realized? How is it taxed if it is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.

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Problem 5

What does a stop order to sell at $$\$ 2$$ mean? When might it be used? What does a limit order to sell at $$\$ 2$$ mean? When might it be used?

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Problem 6

What is the difference between the operation of the margin accounts administered by a clearing house and those administered by a broker?

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Problem 7

What differences exist in the way prices are quoted in the foreign exchange futures market, the foreign exchange spot market, and the foreign exchange forward market?

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Problem 8

The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on. Do these options increase or decrease the futures price? Explain your reasoning.

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Problem 9

What are the most important aspects of the design of a new futures contract?

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Problem 10

Explain how margin accounts protect futures traders against the possibility of default.

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Problem 11

A trader buys two July futures contracts on frozen orange juice concentrate. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $$\$ 6,000$$ per contract, and the maintenance margin is $$\$ 4,5004$$ per contract. What price change would lead to a margin call? Under what circumstances could $$\$ 2,000$$ be withdrawn from the margin account?

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Problem 12

Show that, if the futures price of a commodity is greater than the spot price during the delivery period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures price is less than the spot price? Explain your answer.

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Problem 13

Explain the difference between a market-if-touched order and a stop order.

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Problem 14

Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.

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Problem 15

At the end of one day a clearing house member is long 100 contracts, and the settlement price is $$\$ 50,000$$ per contract. The original margin is $$\$ 2,000$$ per contract. On the following day the member becomes responsible for clearing an additional 20 long contracts, entered into at a price of $$\$ 51,000$$ per contract. The settlement price at the end of this day is $$\$ 50,200$$. How much does the member have to add to its margin account with the exchange clearing house?

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01:19

Problem 16

Explain why collateral requirements will increase in the OTC market as a result of new regulations introduced since the 2008 credit crisis.

Oluwadamilola Ameobi
Oluwadamilola Ameobi
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Problem 17

The forward price of the Swiss franc for delivery in 45 days is quoted as 1.1000 . The futures price for a contract that will be delivered in 45 days is 0.9000 . Explain these two quotes. Which is more favorable for a trader wanting to sell Swiss francs?

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Problem 18

Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.

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02:05

Problem 19

"Speculation in futures markets is pure gambling. It is not in the public interest to allow speculators to trade on a futures exchange." Discuss this viewpoint.

Norman Atentar
Norman Atentar
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Problem 20

Explain the difference between bilateral and central clearing for OTC derivatives.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:03

Problem 21

What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
02:48

Problem 22

"When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one." Explain this statement.

Jennifer Stoner
Jennifer Stoner
Numerade Educator

Problem 23

Suppose that, on October 24, 2018, a company sells one April 2019 live cattle futures contract. It closes out its position on January 21, 2019. The futures price (per pound) is 121.20 cents when it enters into the contract, 118.30 cents when it closes out its position, and 118.80 cents at the end of December 2018. One contract is for the delivery of 40,000 pounds of cattle. What is the total profit? How is it taxed if the company is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.

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03:37

Problem 24

A cattle farmer expects to have 120,000 pounds of live cattle to sell in 3 months. The live cattle futures contract traded by the CME Group is for the delivery of 40,000 pounds of cattle. How can the farmer use the contract for hedging? From the farmer's viewpoint, what are the pros and cons of hedging?

Jennifer Stoner
Jennifer Stoner
Numerade Educator

Problem 25

It is July 2017. A mining company has just discovered a small deposit of gold. It will take 6 months to construct the mine. The gold will then be extracted on a more or less continuous basis for 1 year. Futures contracts on gold are available with delivery months every 2 months from August 2017 to December 2018. Each contract is for the delivery of 100 ounces. Discuss how the mining company might use futures markets for hedging.

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02:29

Problem 26

Explain how CCPs work. What are the advantages to the financial system of requiring CCPs to be used for all standardized derivatives transactions between financial institutions?

Jennifer Stoner
Jennifer Stoner
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Problem 27

Trader A enters into futures contracts to buy 1 million euros for 1.1 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange rate (dollars per euro) declines sharply during the first two months and then increases for the third month to close at 1.1300 . Ignoring daily settlement, what is the total profit of each trader? When the impact of daily settlement is taken into account, which trader has done better?

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Problem 28

Explain what is meant by open interest. Why does the open interest usually decline during the month preceding the delivery month? On a particular day, there were 2,000 trades in a particular futures contract. This means that there were 2,000 buyers (going long) and 2,000 sellers (going short). Of the 2,000 buyers, 1,400 were closing out positions and 600 were entering into new positions. Of the 2,000 sellers, 1,200 were closing out positions and 800 were entering into new positions. What is the impact of the day's trading on open interest?

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Problem 29

One orange juice futures contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2017 a company sells a March 2019 orange juice futures contract for 120 cents per pound. At the end of December 2017, the futures price is 140 cents; at the end of December 2018, it is 110 cents; and in February 2019, it is closed out at 125 cents. The company has a December 31 year end. What is the company's profit or loss on the contract? How is it realized? What is the accounting and tax treatment of the transaction if the company is classified as (a) a hedger and (b) a speculator?

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Problem 30

A company enters into a short futures contract to sell 5,000 bushels of wheat for 750 cents per bushel. The initial margin is $$\$ 3,000$$ and the maintenance margin is $$\$ 2,000$$. What price change would lead to a margin call? Under what circumstances could $$\$ 1,500$$ be withdrawn from the margin account?

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01:02

Problem 31

Suppose that there are no storage costs for crude oil and the interest rate for borrowing or lending is $4 \%$ per annum. How could you make money if the June and December futures contracts for a particular year trade at $$\$ 50$$ and $$\$ 56$$, respectively?

Niamat Khuda
Niamat Khuda
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Problem 32

What position is equivalent to a long forward contract to buy an asset at $K$ on a certain date and a put option to sell it for $K$ on that date.

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Problem 33

A company has derivatives transactions with Banks $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ that are worth $$+\$ 20$$ million, $$-\$ 15$$ million, and $$-\$ 25$$ million, respectively, to the company. How much margin or collateral does the company have to provide in each of the following two situations?
(a) The transactions are cleared bilaterally and are subject to one-way collateral agreements where the company posts variation margin but no initial margin. The banks do not have to post collateral.
(b) The transactions are cleared centrally through the same $\mathrm{CCP}$ and the $\mathrm{CCP}$ requires a total initial margin of $$\$ 10$$ million.

Lainey Roebuck
Lainey Roebuck
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01:16

Problem 34

A bank's derivatives transactions with a counterparty are worth $$+\$ 10$$ million to the bank and are cleared bilaterally. The counterparty has posted $$\$ 10$$ million of cash collateral. What credit exposure does the bank have?

Kaylee Mcclellan
Kaylee Mcclellan
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Problem 35

The author's website (www-2.rotman.utoronto.ca/ hull/data) contains daily closing prices for the crude oil futures contract and the gold futures contract. You are required to download the data for crude oil and answer the following:
(a) Assuming that daily price changes are normally distributed with zero mean, estimate the standard deviation of daily price changes. Calculate the standard deviation of two-day changes from the standard deviation of one-day changes assuming that changes are independent.
(b) Suppose that an exchange wants to set the margin requirement for a member with a long position in one contract so that it is $99 \%$ certain that the margin will not be wiped out by a two-day price move. (It chooses two days because it considers that it can take two days to close out a defaulting member.) How high does the margin have to be when the normal distribution assumption is made? Each contract is on 1,000 barrels of oil.
(c) Use the data to determine how often the margin of the member would actually be wiped out by a two-day price move. What do your results suggest about the appropriateness of the normal distribution assumption?
(d) Suppose that for retail clients the maintenance margin is equal to the amount calculated in (b) and is $75 \%$ of the initial margin. How frequently would the balance in the account of a client with a long position be negative immediately before a margin payment is due (so that the client has an incentive to default)? Assume that balances in excess of the initial margin are withdrawn by the client.

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