, CHAPTER 1
Introduction
Practice Questions
Problem 1.1.
What is the difference between a long forward position and a short forward position?
When a trader enters into a long forward contract, she is agreeing to buy the underlying asset
for a certain price at a certain time in the future. When a trader enters into a short forward
contract, she is agreeing to sell the underlying asset for a certain price at a certain time in
the future.
Problem 1.2.
Explain carefully the difference between hedging, speculation, and arbitrage.
A trader is hedging when she has an exposure to the price of an asset and takes a position in a
derivative to offset the exposure. In a speculation the trader has no exposure to offset. She is
betting on the future movements in the price of the asset. Arbitrage involves taking a position
in two or more different markets to lock in a profit.
Problem 1.3.
What is the difference between entering into a long forward contract when the forward price
is $50 and taking a long position in a call option with a strike price of $50?
In the first case the trader is obligated to buy the asset for $50. (The trader does not have a
choice.) In the second case the trader has an option to buy the asset for $50. (The trader does
not have to exercise the option.)
Problem 1.4.
Explain carefully the difference between selling a call option and buying a put option.
Selling a call option involves giving someone else the right to buy an asset from you. It gives
you a payoff of
−max(ST − K 0) = min(K − ST 0)
Buying a put option involves buying an option from someone else. It gives a payoff of
max(K − ST 0)
In both cases the potential payoff is K − ST . When you write a call option, the payoff is
negative or zero. (This is because the counterparty chooses whether to exercise.) When you
buy a put option, the payoff is zero or positive. (This is because you choose whether to
exercise.)
Problem 1.5.
An investor enters into a short forward contract to sell 100,000 British pounds for US
dollars at an exchange rate of 1.5000 US dollars per pound. How much does the investor
gain or lose if the exchange rate at the end of the contract is (a) 1.4900 and (b) 1.5200?
, (a) The investor is obligated to sell pounds for 1.5000 when they are worth 1.4900. The
gain is (1.5000−1.4900) ×100,000 = $1,000.
(b) The investor is obligated to sell pounds for 1.5000 when they are worth 1.5200. The
loss is (1.5200−1.5000)×100,000 = $2,000
Problem 1.6.
A trader enters into a short cotton futures contract when the futures price is 50 cents per
pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or
lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents
per pound?
(a) The trader sells for 50 cents per pound something that is worth 48.20 cents per pound.
Gain = ($05000 −$04820)50 000 = $900 .
(b) The trader sells for 50 cents per pound something that is worth 51.30 cents per pound.
Loss = ($05130 −$05000)50 000 = $650 .
Problem 1.7.
Suppose that you write a put contract with a strike price of $40 and an expiration date in
three months. The current stock price is $41 and the contract is on 100 shares. What have
you committed yourself to? How much could you gain or lose?
You have sold a put option. You have agreed to buy 100 shares for $40 per share if the party
on the other side of the contract chooses to exercise the right to sell for this price. The option
will be exercised only when the price of stock is below $40. Suppose, for example, that the
option is exercised when the price is $30. You have to buy at $40 shares that are worth $30;
you lose $10 per share, or $1,000 in total. If the option is exercised when the price is $20, you
lose $20 per share, or $2,000 in total. The worst that can happen is that the price of the stock
declines to almost zero during the three-month period. This highly unlikely event would cost
you $4,000. In return for the possible future losses, you receive the price of the option from
the purchaser.
Problem 1.8.
What is the difference between the over-the-counter market and the exchange-traded market?
What are the bid and offer quotes of a market maker in the over-the-counter market?
The over-the-counter market is a telephone- and computer-linked network of financial
institutions, fund managers, and corporate treasurers where two participants can enter into
any mutually acceptable contract. An exchange-traded market is a market organized by an
exchange where the contracts that can be traded have been defined by the exchange. When a
market maker quotes a bid and an offer, the bid is the price at which the market maker is
prepared to buy and the offer is the price at which the market maker is prepared to sell.
Problem 1.9.
You would like to speculate on a rise in the price of a certain stock. The current stock price is
$29, and a three-month call with a strike of $30 costs $2.90. You have $5,800 to invest.
, Identify two alternative strategies, one involving an investment in the stock and the other
involving investment in the option. What are the potential gains and losses from each?
One strategy would be to buy 200 shares. Another would be to buy 2,000 options. If the share
price does well the second strategy will give rise to greater gains. For example, if the share
price goes up to $40 you gain [2000($40 −$30)] −$5800 = $14 200 from the second
strategy and only 200($40 −$29) = $2 200 from the first strategy. However, if the share
price does badly, the second strategy gives greater losses. For example, if the share price goes
down to $25, the first strategy leads to a loss of 200($29 −$25) = $800 whereas the second
strategy leads to a loss of the whole $5,800 investment. This example shows that options
contain built in leverage.
Problem 1.10.
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to
provide you with insurance against a decline in the value of your holding over the next four
months?
You could buy 50 put option contracts (each on 100 shares) with a strike price of $25 and an
expiration date in four months. If at the end of four months the stock price proves to be less
than $25, you can exercise the options and sell the shares for $25 each.
Problem 1.11.
When first issued, a stock provides funds for a company. Is the same true of an exchange-
traded stock option? Discuss.
An exchange-traded stock option provides no funds for the company. It is a security sold by
one investor to another. The company is not involved. By contrast, a stock when it is first
issued is sold by the company to investors and does provide funds for the company.
Problem 1.12.
Explain why a futures contract can be used for either speculation or hedging.
If an investor has an exposure to the price of an asset, he or she can hedge with futures
contracts. If the investor will gain when the price decreases and lose when the price increases,
a long futures position will hedge the risk. If the investor will lose when the price decreases
and gain when the price increases, a short futures position will hedge the risk. Thus either a
long or a short futures position can be entered into for hedging purposes.
If the investor has no exposure to the price of the underlying asset, entering into a futures
contract is speculation. If the investor takes a long position, he or she gains when the asset’s
price increases and loses when it decreases. If the investor takes a short position, he or she
loses when the asset’s price increases and gains when it decreases.
Problem 1.13.
Suppose that a March call option to buy a share for $50 costs $2.50 and is held until March.
Under what circumstances will the holder of the option make a profit? Under what
circumstances will the option be exercised? Draw a diagram showing how the profit on a
long position in the option depends on the stock price at the maturity of the option.
The holder of the option will gain if the price of the stock is above $52.50 in March. (This
ignores the time value of money.) The option will be exercised if the price of the stock is
Introduction
Practice Questions
Problem 1.1.
What is the difference between a long forward position and a short forward position?
When a trader enters into a long forward contract, she is agreeing to buy the underlying asset
for a certain price at a certain time in the future. When a trader enters into a short forward
contract, she is agreeing to sell the underlying asset for a certain price at a certain time in
the future.
Problem 1.2.
Explain carefully the difference between hedging, speculation, and arbitrage.
A trader is hedging when she has an exposure to the price of an asset and takes a position in a
derivative to offset the exposure. In a speculation the trader has no exposure to offset. She is
betting on the future movements in the price of the asset. Arbitrage involves taking a position
in two or more different markets to lock in a profit.
Problem 1.3.
What is the difference between entering into a long forward contract when the forward price
is $50 and taking a long position in a call option with a strike price of $50?
In the first case the trader is obligated to buy the asset for $50. (The trader does not have a
choice.) In the second case the trader has an option to buy the asset for $50. (The trader does
not have to exercise the option.)
Problem 1.4.
Explain carefully the difference between selling a call option and buying a put option.
Selling a call option involves giving someone else the right to buy an asset from you. It gives
you a payoff of
−max(ST − K 0) = min(K − ST 0)
Buying a put option involves buying an option from someone else. It gives a payoff of
max(K − ST 0)
In both cases the potential payoff is K − ST . When you write a call option, the payoff is
negative or zero. (This is because the counterparty chooses whether to exercise.) When you
buy a put option, the payoff is zero or positive. (This is because you choose whether to
exercise.)
Problem 1.5.
An investor enters into a short forward contract to sell 100,000 British pounds for US
dollars at an exchange rate of 1.5000 US dollars per pound. How much does the investor
gain or lose if the exchange rate at the end of the contract is (a) 1.4900 and (b) 1.5200?
, (a) The investor is obligated to sell pounds for 1.5000 when they are worth 1.4900. The
gain is (1.5000−1.4900) ×100,000 = $1,000.
(b) The investor is obligated to sell pounds for 1.5000 when they are worth 1.5200. The
loss is (1.5200−1.5000)×100,000 = $2,000
Problem 1.6.
A trader enters into a short cotton futures contract when the futures price is 50 cents per
pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or
lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents
per pound?
(a) The trader sells for 50 cents per pound something that is worth 48.20 cents per pound.
Gain = ($05000 −$04820)50 000 = $900 .
(b) The trader sells for 50 cents per pound something that is worth 51.30 cents per pound.
Loss = ($05130 −$05000)50 000 = $650 .
Problem 1.7.
Suppose that you write a put contract with a strike price of $40 and an expiration date in
three months. The current stock price is $41 and the contract is on 100 shares. What have
you committed yourself to? How much could you gain or lose?
You have sold a put option. You have agreed to buy 100 shares for $40 per share if the party
on the other side of the contract chooses to exercise the right to sell for this price. The option
will be exercised only when the price of stock is below $40. Suppose, for example, that the
option is exercised when the price is $30. You have to buy at $40 shares that are worth $30;
you lose $10 per share, or $1,000 in total. If the option is exercised when the price is $20, you
lose $20 per share, or $2,000 in total. The worst that can happen is that the price of the stock
declines to almost zero during the three-month period. This highly unlikely event would cost
you $4,000. In return for the possible future losses, you receive the price of the option from
the purchaser.
Problem 1.8.
What is the difference between the over-the-counter market and the exchange-traded market?
What are the bid and offer quotes of a market maker in the over-the-counter market?
The over-the-counter market is a telephone- and computer-linked network of financial
institutions, fund managers, and corporate treasurers where two participants can enter into
any mutually acceptable contract. An exchange-traded market is a market organized by an
exchange where the contracts that can be traded have been defined by the exchange. When a
market maker quotes a bid and an offer, the bid is the price at which the market maker is
prepared to buy and the offer is the price at which the market maker is prepared to sell.
Problem 1.9.
You would like to speculate on a rise in the price of a certain stock. The current stock price is
$29, and a three-month call with a strike of $30 costs $2.90. You have $5,800 to invest.
, Identify two alternative strategies, one involving an investment in the stock and the other
involving investment in the option. What are the potential gains and losses from each?
One strategy would be to buy 200 shares. Another would be to buy 2,000 options. If the share
price does well the second strategy will give rise to greater gains. For example, if the share
price goes up to $40 you gain [2000($40 −$30)] −$5800 = $14 200 from the second
strategy and only 200($40 −$29) = $2 200 from the first strategy. However, if the share
price does badly, the second strategy gives greater losses. For example, if the share price goes
down to $25, the first strategy leads to a loss of 200($29 −$25) = $800 whereas the second
strategy leads to a loss of the whole $5,800 investment. This example shows that options
contain built in leverage.
Problem 1.10.
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to
provide you with insurance against a decline in the value of your holding over the next four
months?
You could buy 50 put option contracts (each on 100 shares) with a strike price of $25 and an
expiration date in four months. If at the end of four months the stock price proves to be less
than $25, you can exercise the options and sell the shares for $25 each.
Problem 1.11.
When first issued, a stock provides funds for a company. Is the same true of an exchange-
traded stock option? Discuss.
An exchange-traded stock option provides no funds for the company. It is a security sold by
one investor to another. The company is not involved. By contrast, a stock when it is first
issued is sold by the company to investors and does provide funds for the company.
Problem 1.12.
Explain why a futures contract can be used for either speculation or hedging.
If an investor has an exposure to the price of an asset, he or she can hedge with futures
contracts. If the investor will gain when the price decreases and lose when the price increases,
a long futures position will hedge the risk. If the investor will lose when the price decreases
and gain when the price increases, a short futures position will hedge the risk. Thus either a
long or a short futures position can be entered into for hedging purposes.
If the investor has no exposure to the price of the underlying asset, entering into a futures
contract is speculation. If the investor takes a long position, he or she gains when the asset’s
price increases and loses when it decreases. If the investor takes a short position, he or she
loses when the asset’s price increases and gains when it decreases.
Problem 1.13.
Suppose that a March call option to buy a share for $50 costs $2.50 and is held until March.
Under what circumstances will the holder of the option make a profit? Under what
circumstances will the option be exercised? Draw a diagram showing how the profit on a
long position in the option depends on the stock price at the maturity of the option.
The holder of the option will gain if the price of the stock is above $52.50 in March. (This
ignores the time value of money.) The option will be exercised if the price of the stock is
