Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
,Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
CHAPTER 1
Introduction
Short Concept Questions
Practice Questions
1.1
Selling a call option involves giving someone else the right to buy an asset from you. It gives
you a payoff of
−max(ST − K0) = 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.)
1.2
(a) The investor is obligated to sell pounds for 1.3000 when they are worth 1.2900. The
gain is (1.3000—1.2900) ×100,000 = $1,000.
(b) The investor is obligated to sell pounds for 1.3000 when they are worth 1.3200. The
loss is (1.3200—1.3000)×100,000 = $2,000
1.3
(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 .
1.4
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.
1.5
One strategy would be to buy 200 shares. Another would be to buy 2,000 options. If the share
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
,Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
price does well, the second strategy will give rise to greater gains. For example, if the share
price goes up to $40 you gain [2 000($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.
1.6
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.
1.7
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.
1.8
If a trader has an exposure to the price of an asset, a hedge with futures contracts can be used.
If the trader will gain when the price decreases and lose when the price increases, a long
futures position will hedge the risk. If the trader 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 trader has no exposure to the price of the underlying asset, entering into a futures
contract is speculation. If the trader takes a long position, there is a gain when the asset’s
price increases and a loss when it decreases. If the trader takes a short position, there is a loss
when the asset’s price increases and a gain when it decreases.
1.9
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
above $50.00 in March. The profit as a function of the stock price is shown in Figure S1.1.
Figure S1.1: Profit from long position in Problem 1.9
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
, Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
1.10
The seller of the option will lose money if the price of the stock is below $56.00 in June.
(This ignores the time value of money.) The option will be exercised if the price of the stock
is below $60.00 in June. The profit as a function of the stock price is shown in Figure S1.2.
Figure S1.2: Profit from short position in Problem 1.10
1.11
The trader has an inflow of $2 in May and an outflow of $5 in September. The $2 is the cash
received from the sale of the option. The $5 is the result of the option being exercised. The
trader has to buy the stock for $25 in September and sell it to the purchaser of the option for
$20.
1.12
The trader makes a gain if the price of the stock is above $26 at the time of exercise. (This
ignores the time value of money.)
1.13
A long position in a four-month put option on the foreign currency can provide insurance
against the exchange rate falling below the strike price. It ensures that the foreign currency
can be sold for at least the strike price.
1.14
The company could enter into a long forward contract to buy 1 million Canadian dollars in
six months. This would have the effect of locking in an exchange rate equal to the current
forward exchange rate. Alternatively, the company could buy a call option giving it the right
(but not the obligation) to purchase 1 million Canadian dollars at a certain exchange rate in
six months. This would provide insurance against a strong Canadian dollar in six months
while still allowing the company to benefit from a weak Canadian dollar at that time.
1.15
a) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0084
per yen. The gain is 100 00006 millions of dollars or $60,000.
b) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0101
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
,Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
CHAPTER 1
Introduction
Short Concept Questions
Practice Questions
1.1
Selling a call option involves giving someone else the right to buy an asset from you. It gives
you a payoff of
−max(ST − K0) = 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.)
1.2
(a) The investor is obligated to sell pounds for 1.3000 when they are worth 1.2900. The
gain is (1.3000—1.2900) ×100,000 = $1,000.
(b) The investor is obligated to sell pounds for 1.3000 when they are worth 1.3200. The
loss is (1.3200—1.3000)×100,000 = $2,000
1.3
(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 .
1.4
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.
1.5
One strategy would be to buy 200 shares. Another would be to buy 2,000 options. If the share
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
,Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
price does well, the second strategy will give rise to greater gains. For example, if the share
price goes up to $40 you gain [2 000($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.
1.6
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.
1.7
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.
1.8
If a trader has an exposure to the price of an asset, a hedge with futures contracts can be used.
If the trader will gain when the price decreases and lose when the price increases, a long
futures position will hedge the risk. If the trader 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 trader has no exposure to the price of the underlying asset, entering into a futures
contract is speculation. If the trader takes a long position, there is a gain when the asset’s
price increases and a loss when it decreases. If the trader takes a short position, there is a loss
when the asset’s price increases and a gain when it decreases.
1.9
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
above $50.00 in March. The profit as a function of the stock price is shown in Figure S1.1.
Figure S1.1: Profit from long position in Problem 1.9
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
, Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
1.10
The seller of the option will lose money if the price of the stock is below $56.00 in June.
(This ignores the time value of money.) The option will be exercised if the price of the stock
is below $60.00 in June. The profit as a function of the stock price is shown in Figure S1.2.
Figure S1.2: Profit from short position in Problem 1.10
1.11
The trader has an inflow of $2 in May and an outflow of $5 in September. The $2 is the cash
received from the sale of the option. The $5 is the result of the option being exercised. The
trader has to buy the stock for $25 in September and sell it to the purchaser of the option for
$20.
1.12
The trader makes a gain if the price of the stock is above $26 at the time of exercise. (This
ignores the time value of money.)
1.13
A long position in a four-month put option on the foreign currency can provide insurance
against the exchange rate falling below the strike price. It ensures that the foreign currency
can be sold for at least the strike price.
1.14
The company could enter into a long forward contract to buy 1 million Canadian dollars in
six months. This would have the effect of locking in an exchange rate equal to the current
forward exchange rate. Alternatively, the company could buy a call option giving it the right
(but not the obligation) to purchase 1 million Canadian dollars at a certain exchange rate in
six months. This would provide insurance against a strong Canadian dollar in six months
while still allowing the company to benefit from a weak Canadian dollar at that time.
1.15
a) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0084
per yen. The gain is 100 00006 millions of dollars or $60,000.
b) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0101
Solution Manual for Options, Future and Other Derivatives 11th Edition by John Hull, Sankarshan Basu
