CHAPTER 10
Mechanics of Options Markets
Practice Questions
Problem 10.1.
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 exercid? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.
The investor makes a profit if the price of the stock on the expiration date is less than $37. In the circumstances the gain from exercising the option is greater than $3. The option will be exercid if the stock price is less than $40 at the maturity of the option. The variation of the investor’s profit with the s tock price in Figure S10.1.
Figure S10.1: Investor’s profit in Problem 10.1
Problem 10.2.
An investor lls 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 exercid? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.
The investor makes a profit if the price of the stock is below $54 on the expiration date. If the stock price is below $50, the option will not be exercid, and the investor makes a profit of $4. If the stock price is between $50 and $54, the option is exercid and the investor makes a profit between $0 and $4. The variation of the investor’s profit with the stoc k price is as
shown in Figure S10.2.
Figure S10.2: Investor’s profit in Problem 10.2难过的句子
Problem 10.3.
An investor lls a European call option with strike price of K and maturity T and buys a put with the sam e strike price and maturity. Describe the investor’s position.
The payoff to the investor is
max (0)max (0)T T S K K S --,+-,
This is T K S - in all circumstances. The investor’s position is the same as a short position in a forward contract with delivery price K .
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Problem 10.4.
Explain why margin accounts are required when clients write options but not when they buy options.
When an investor buys an option, cash must be paid up front. There is no possibility of future liabilities and therefore no need for a margin account. When an investor lls an option, there are potential future liabilities. To protect against the risk of a default, margins are required.
Problem 10.5.
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A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30?
一键局域网共享On April 1 options trade with expiration months of April, May, August, and November. On May 30 options trade with expiration months of June, July, August, and November.
Problem 10.6.
A company declares a 2-for-1 stock split. Explain how the terms change for a call option with
a strike price of $60.
The strike price is reduced to $30, and the option gives the holder the right to purcha twice as many shares.
Problem 10.7.
“Employee stock options issued by a company are different from regular exchange-traded call option
s on the company’s stock becau they can affect the capital structure of the company.” Explain this statement.
The exerci of employee stock options usually leads to new shares being issued by the company and sold to the employee. This changes the amount of equity in the capital structure. When a regular exchange-traded option is exercid no new shares are issued and the company’s capital structure is not affected.
Problem 10.8.
A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-counter market for trading?
The NASDAQ OMX offers options with standard strike prices and times to maturity. Options in the over-the-counter market have the advantage that they can be tailored to meet the preci needs of the treasurer. Their disadvantage is that they expo the treasurer to some credit risk. Exchanges organize their trading so that there is virtually no credit risk.
Problem 10.9.
Suppo 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 exercid? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.
Ignoring the time value of money, the holder of the option will make a profit if the stock price at maturity of the option is greater than $105. This is becau the payoff to the holder of the option is, in the circumstances, greater than the $5 paid for the option. The option will be exercid if the stock price at maturity is greater than $100. Note that if the stock price is between $100 and $105 the option is exercid, but the holder of the option takes a loss overall. The profit from a long position is as shown in Figure S10.3.
Figure S10.3:Profit from long position in Problem 10.9枉自
Problem 10.10.
Suppo that a European put option to ll a share for $60 costs $8 and is held until maturity. Under what circumstances will the ller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercid? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.
Ignoring the time value of money, the ller of the option will make a profit if the stock price at maturity is greater than $52.00. This is becau the cost to the ller of the option is in the circumstances less than the price received for the option. The option will be exercid if the stock price at maturity is less than $60.00. Note that if the stock price is between $52.00 and $60.00 the ller of the option makes a profit even though the option is exercid. The profit from the short position is as shown in Figure S10.4.
Figure S10.4:Profit from short position in Problem 10.10
揭后语Problem 10.11.
Describe the terminal value of the following portfolio: a newly entered-into long forward contract on a
n ast and a long position in a European put option on the ast with the same maturity as the forward contract and a strike price that is equal to the forward price of the ast at the time the portfolio is t up. Show that the European put option has the same value as a European call option with the same strike price and maturity.
The terminal value of the long forward contract is:
0T S F -
where T S is the price of the ast at maturity and 0F is the forward price of the ast at the
time the portfolio is t up. (The delivery price in the forward contract is also 0F .)
The terminal value of the put option is:
0max (0)T F S -,
The terminal value of the portfolio is therefore
00max (0)T T S F F S -+-,
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0max (0]T S F =,-
This is the same as the terminal value of a European call option with the same maturity as the forward contract and an exerci price equal to 0F . This result is illustrated in the Figure S10.5.
Figure S10.5: Profit from portfolio in Problem 10.11
We have shown that the forward contract plus the put is worth the same as a call with the same strike price and time to maturity as the put. The forward contract is worth zero at the time the portfolio is t up. It follows that the put is worth the same as the call at the time the portfolio is t up.
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