SOLUTION MANUAL
All Chapters Included
, 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 ($0 5000 $0 4820) 50 000 $900 .
(b) The trader sells for 50 cents per pound something that is worth 51.30
cents per pound. Loss ($0 5130 $0 5000) 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.
All Chapters Included
, 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 ($0 5000 $0 4820) 50 000 $900 .
(b) The trader sells for 50 cents per pound something that is worth 51.30
cents per pound. Loss ($0 5130 $0 5000) 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.
