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Options, Futures, and Other Derivatives

John C. Hull

Chapter 10

Mechanics of options markets - all with Video Answers

Educators

Chapter Questions

Problem 1

An investor buys a European put on a share for $$\$ 3$$. The stock price is $$\$ 42$$ and the strike price is $$\$ 40$$. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor's profit with the stock price at the maturity of the option.

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Problem 2

An investor sells a European call on a share for $$\$ 4$$. The stock price is $$\$ 47$$ and the strike price is $$\$ 50$$. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor's profit with the stock price at the maturity of the option.

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04:10

Problem 3

An investor sells a European call option with strike price of $K$ and maturity $T$ and buys a put with the same strike price and maturity. Describe the investor's position.

Narayan Hari
Narayan Hari
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Problem 4

Explain why margin accounts are required when clients write options but not when they buy options.

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Problem 5

A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30 ?

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Problem 6

A company declares a 2 -for-1 stock split. Explain how the terms change for a call option with a strike price of $$\$ 60$$.

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Problem 7

"Employee stock options issued by a company are different from regular exchangetraded call options on the company's stock because they can affect the capital structure of the company." Explain this statement.

James Kiss
James Kiss
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Problem 8

A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) NASDAQ OMX and (b) the over-thecounter market for trading?

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Problem 9

Suppose that a European call option to buy a share for $$\$ 100.00$$ costs $$\$ 5.00$$ and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.

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Problem 10

Suppose that a European put option to sell a share for $$\$ 60$$ costs $$\$ 8$$ and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.

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04:10

Problem 11

Describe the terminal value of the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that the European put option has the same value as a European call option with the same strike price and maturity.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 12

A trader buys a call option with a strike price of $$\$ 45$$ and a put option with a strike price of $$\$ 40$$. Both options have the same maturity. The call costs $$\$ 3$$ and the put costs $$\$ 4$$. Draw a diagram showing the variation of the trader's profit with the asset price.

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Problem 13

Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.

Rashmi Sinha
Rashmi Sinha
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Problem 14

Explain why an American option is always worth at least as much as its intrinsic value.

Rashmi Sinha
Rashmi Sinha
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Problem 15

Explain carefully the difference between writing a put option and buying a call option.

Rashmi Sinha
Rashmi Sinha
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Problem 16

The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation's foreign exchange risk. Discuss the advantages and disadvantages of each.

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Problem 17

Consider an exchange-traded call option contract to buy 500 shares with a strike price of $$\$ 40$$ and maturity in 4 months. Explain how the terms of the option contract change when there is: (a) a $10 \%$ stock dividend; (b) a $10 \%$ cash dividend; and (c) a 4 -for-1 stock split.

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03:18

Problem 18

"If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months." Discuss this statement.

Pragya Ahuja
Pragya Ahuja
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05:30

Problem 19

What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price?

Jennifer Stoner
Jennifer Stoner
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Problem 20

Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, and (c) August 5?

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03:12

Problem 21

Explain why the market maker's bid-offer spread represents a real cost to options investors.

Jennifer Stoner
Jennifer Stoner
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Problem 22

A U.S. investor writes five naked call option contracts. The option price is $$\$ 3.50$$, the strike price is $$\$ 60.00$$, and the stock price is $$\$ 57.00$$. What is the initial margin requirement?

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Problem 23

Calculate the intrinsic value and time value from the mid market (average of bid and offer) prices for the September call options in Table 1.2. Do the same for the September put options in Table 1.3. Assume in each case that the current mid market stock price is $$\$ 696.00$$.

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Problem 24

A trader has a put option contract to sell 100 shares of a stock for a strike price of $$\$ 60$$. What is the effect on the terms of the contract of
(a) A $$\$ 2$$ dividend being declared
(b) A $$\$ 2$$ dividend being paid
(c) A 5 -for-2 stock split
(d) A $5 \%$ stock dividend being paid.

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Problem 25

A trader writes 5 naked put option contracts with each contract being on 100 shares. The option price is $$\$ 10$$, the time to maturity is 6 months, and the strike price is $$\$ 64$$.
(a) What is the margin requirement if the stock price is $$\$ 58$$ ?
(b) How would the answer to (a) change if the rules for index options applied?
(c) How would the answer to (a) change if the stock price were $$\$ 70$$ ?
(d) How would the answer to (a) change if the trader is buying instead of selling the options?

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Problem 26

The price of a stock is $$\$ 40$$. The price of a l-year European put option on the stock with a strike price of $$\$ 30$$ is quoted as $$\$ 7$$ and the price of a 1-year European call option on the stock with a strike price of $$\$ 50$$ is quoted as $$\$ 5$$. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor's profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?

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00:43

Problem 27

"If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense." Discuss this viewpoint. Can you think of alternatives to the usual employee stock option plan that take the viewpoint into account.

Amrita Bhasin
Amrita Bhasin
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Problem 28

Use DerivaGem to calculate the value of an American put option on a non-dividendpaying stock when the stock price is $$\$ 30$$, the strike price is $$\$ 32$$, the risk-free rate is $5 \%$, the volatility is $30 \%$, and the time to maturity is 1.5 years. (Choose "Binomial American" for the "option type" and 50 time steps.)
(a) What is the option's intrinsic value?
(b) What is the option's time value?
(c) What would a time value of zero indicate? What is the value of an option with zero time value?
(d) Using a trial and error approach, calculate how low the stock price would have to be for the time value of the option to be zero.

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02:32

Problem 29

10.29. On July 20,2004 , Microsoft surprised the market by announcing a $$\$ 3$$ dividend. The exdividend date was November 17, 2004, and the payment date was December 2, 2004. Its stock price at the time was about $$\$ 28$$. It also changed the terms of its employee stock options so that each exercise price was adjusted downward to
$$
\text { Predividend exercise price } \times \frac{\text { Closing price }-\$ 3.00}{\text { Closing price }}
$$
The number of shares covered by each stock option outstanding was adjusted upward to
$$
\text { Number of shares predividend } \times \frac{\text { Closing price }}{\text { Closing price }-\$ 3.00}
$$
"Closing Price" means the official NASDAQ closing price of a share of Microsoft common stock on the last trading day before the ex-dividend date. Evaluate this adjustment. Compare it with the system used by exchanges to adjust for extraordinary dividends (see Business Snapshot 10.1).

Nick Johnson
Nick Johnson
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