Options, Futures, and Other Derivatives

John C. Hull

Chapter 8

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.

Jodi Folley

Jodi Folley

Numerade Educator

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.

Pragya Ahuja

Numerade Educator

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

Numerade Educator

Problem 4

Explain why brokers require margins when clients write options but not when they buy options.

Tommy Nguyen

Numerade Educator

Problem 5

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

Arulmozhi T

Numerade Educator

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 $\$ 60$.

Akash M

Numerade Educator

Problem 7

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

Riham Bassal

Numerade Educator

Problem 8

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

Pragya Ahuja

Numerade Educator

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.

Jodi Folley

Numerade Educator

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.

Jodi Folley

Numerade Educator

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

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 $\$ 4 .$ 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.

Jodi Folley

Numerade Educator

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

Numerade Educator

Problem 14

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

Rashmi Sinha

Numerade Educator

Problem 15

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

Rashmi Sinha

Numerade Educator

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.

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

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.

Nick Johnson

Numerade Educator

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

Numerade Educator

Problem 19

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

Rashmi Sinha

Numerade Educator

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?

James Kiss

Numerade Educator

Problem 21

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

Nick Johnson

Numerade Educator

Problem 22

A United States 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?

Kari Hasz

Numerade Educator

Problem 23

The price of a stock is $\$ 40 .$ The price of a 1 -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?

Jodi Folley

Numerade Educator

Problem 24

"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

Numerade Educator

Problem 25

Use DerivaGem to calculate the value of an American put option on a non-dividend. paying 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.

Md.Daniyal Arshad

Md.Daniyal Arshad

Numerade Educator

Problem 26

On July $20,2004,$ Microsoft surprised the market by announcing a $\$ 3$ dividend. The ex. dividend 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 empioyee stock options so that each exercise price was adjusted downward to
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
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 8.1 ).

Nick Johnson

Numerade Educator