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actively traded contracts on the CBOE. Together, these contracts dominate CBOE volume.

Futures options Futures options give their holders the right to buy or sell a specified fu-
tures contract, using as a futures price the exercise price of the option. Although the delivery
process is slightly complicated, the terms of futures options contracts are designed in effect to
allow the option to be written on the future price itself. The option holder receives upon exer-
cise net proceeds equal to the difference between the current futures price on the specified asset
and the exercise price of the option. Thus, if the futures price is, say, $37, and the call has an ex-
ercise price of $35, the holder who exercises the call option on the futures gets a payoff of $2.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




497
14 Options Markets




F I G U R E 14.2
Index options
Note: Prices are for February 26, 2001.
Source: The Wall Street Journal, February 27, 2001. Reprinted by permission of The Wall Street Journal, © 2001 Dow Jones & Company, Inc. All Rights
Reserved Worldwide.




Foreign currency options A currency option offers the right to buy or sell a quantity
of foreign currency for a specified amount of domestic currency. Currency option contracts
call for purchase or sale of the currency in exchange for a specified number of U.S. dollars.
Contracts are quoted in cents or fractions of a cent per unit of foreign currency.
There is an important difference between currency options and currency futures options.
The former provide payoffs that depend on the difference between the exercise price and the
exchange rate at maturity. The latter are foreign exchange futures options that provide payoffs
that depend on the difference between the exercise price and the exchange rate futures price at
maturity. Because exchange rates and exchange rate futures prices generally are not equal, the
options and futures-options contracts will have different values, even with identical expiration
dates and exercise prices. Today, trading volume in currency futures options dominates by far
trading in currency options.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




498 Part FIVE Derivative Markets


Interest rate options Options also are traded on Treasury notes and bonds, Treasury
bills, certificates of deposit, GNMA pass-through certificates, and yields on Treasury securi-
ties of various maturities. Options on several interest rate futures also are traded. Among them
are contracts on Treasury bond, Treasury note, municipal bond, LIBOR, Eurodollar, and
British and euro-denominated interest rates.

14.2 VALUES OF OPTIONS AT EXPIRATION
Call Options
Recall that a call option gives the right to purchase a security at the exercise price. If you hold
a call option on Microsoft stock with an exercise price of $60, and Microsoft is now selling at
$70, you can exercise your option to purchase the stock at $60 and simultaneously sell the
shares at the market price of $70, clearing $10 per share. Yet if the shares sell below $60, you
can sit on the option and do nothing, realizing no further gain or loss. The value of the call op-
tion at expiration equals
Payoff to call holder at expiration ST X if ST X
0 if ST X
where ST is the value of the stock at the expiration date, and X is the exercise price. This for-
mula emphasizes the option property because the payoff cannot be negative. That is, the op-
tion is exercised only if ST exceeds X. If ST is less than X, exercise does not occur, and the
option expires with zero value. The loss to the option holder in this case equals the price orig-
inally paid. More generally, the profit to the option holder is the payoff to the option minus the
original purchase price.
The value at expiration of the call on Microsoft with exercise price $60 is given by the fol-
lowing schedule.

Microsoft value $50 $60 $70 $80 $90
Option value 0 0 10 20 30

For Microsoft prices at or below $60, the option expires worthless. Above $60, the option
is worth the excess of Microsoft™s price over $60. The option™s value increases by one dollar
for each dollar increase in the Microsoft stock price. This relationship can be depicted graph-
ically, as in Figure 14.3.



F I G U R E 14.3 $30
Payoff and profit to
Payoff = Value at expiration
call option at
$20
expiration

$10


ST
0
40 50 60 70 80
Cost of option Profit
“$10
“$14
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




499
14 Options Markets


The solid line in Figure 14.3 depicts the value of the call at expiration. The net profit to the
holder of the call equals the gross payoff less the initial investment in the call. Suppose the call
cost $14. Then the profit to the call holder would be as given in the dashed (bottom) line of
Figure 14.3. At option expiration, the investor has suffered a loss of $14 if the stock price is
less than or equal to $60.
Profits do not become positive unless the stock price at expiration exceeds $74. The break-
even point is $74, because at that price the payoff to the call, ST X $74 $60 $14,
equals the cost paid to acquire the call. Hence, the call holder shows a profit only if the stock
price is higher.
Conversely, the writer of the call incurs losses if the stock price is high. In that scenario, the
writer will receive a call and will be obligated to deliver a stock worth ST for only X dollars.
Payoff to call writer (ST X) if ST X
0 if ST X
The call writer, who is exposed to losses if Microsoft increases in price, is willing to bear this
risk in return for the option premium.
Figure 14.4 depicts the payoff and profit diagrams for the call writer. These are the mirror
images of the corresponding diagrams for call holders. The break-even point for the option
writer also is $74. The (negative) payoff at that point just offsets the premium originally re-
ceived when the option was written.

Put Options
A put option conveys the right to sell an asset at the exercise price. In this case, the holder will
not exercise the option unless the asset sells for less than the exercise price. For example, if
Microsoft shares were to fall to $60, a put option with exercise price $70 could be exercised
to give a $10 payoff to its holder. The holder would purchase a share of Microsoft for $60 and
simultaneously deliver it to the put option writer for the exercise price of $70.
The value of a put option at expiration is
Payoff to put holder 0 if ST X
X ST if ST X
The solid line in Figure 14.5 illustrates the payoff at maturity to the holder of a put option
on Microsoft stock with an exercise price of $60. If the stock price at option maturity is above



F I G U R E 14.4
Payoff and profit to
call writers at
$14 expiration

ST
0
$60 $74
Profit




Payoff
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




500 Part FIVE Derivative Markets




F I G U R E 14.5
Payoff and profit to put
option at expiration $60




Payoff = Value of put at expiration
Profit


Price of put
ST
0
$60




$60, the put has no value, as the right to sell the shares at $60 would not be exercised. Below
a price of $60, the put value at expiration increases by $1 for each dollar the stock price falls.
The dashed line in Figure 14.5 is a graph of the put option owner™s profit at expiration, net of
the initial cost of the put.
Writing puts naked (i.e., writing a put without an offsetting short position in the stock for
hedging purposes) exposes the writer to losses if the market falls. Writing naked out-of-the-
money puts was once considered an attractive way to generate income, as it was believed that
as long as the market did not fall sharply before the option expiration, the option premium
could be collected without the put holder ever exercising the option against the writer. Be-
cause only sharp drops in the market could result in losses to the writer of the put, the strategy
was not viewed as overly risky. However, the nearby box notes that in the wake of the market
crash of October 1987, such put writers suffered huge losses. Participants now perceive much
greater risk to this strategy.


>
2. Consider these four option strategies: (i) buy a call; (ii) write a call; (iii) buy a put;
Concept
(iv) write a put.
CHECK a. For each strategy, plot both the payoff and profit diagrams as a function of the
final stock price.
b. Why might one characterize both buying calls and writing puts as “bullish”
strategies? What is the difference between them?
c. Why might one characterize both buying puts and writing calls as “bearish”
strategies? What is the difference between them?


Options versus Stock Investments
Purchasing call options is a bullish strategy; that is, the calls provide profits when stock prices
increase. Purchasing puts, in contrast, is a bearish strategy. Symmetrically, writing calls is
bearish, while writing puts is bullish. Because option values depend on the price of the under-
lying stock, the purchase of options may be viewed as a substitute for direct purchase or sale
of a stock. Why might an option strategy be preferable to direct stock transactions? We can
begin to answer this question by comparing the values of option versus stock positions in
Microsoft.
Suppose you believe Microsoft stock will increase in value from its current level, which we
will round off to $70. You know your analysis could be incorrect, however, and that Microsoft
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




The Black Hole: Puts and the Market Crash
THEIR SALES OF “NAKED PUTS” QUICKLY expires. These contracts are usually sold “out of the
money””priced at a level below current market prices
COME TO GRIEF, DAMAGE SUITS ARE
that makes it unprofitable to exercise the option so long
FILED
as the market rises or stays flat. The seller pockets a
When Robert O™Connor got involved in stock-index op- small amount per contract.
tions, he hoped his trading profits would help put his But if the market plunges, as it did October 19, the
children through college. His broker, Mr. O™Connor ex- option swings into the money. The seller, in effect, has
plains, “said we would make about $1,000 a month, to pay pre-plunge stock prices to make good on his
and if our losses got to $2,000 to $3,000, he would contract”and he takes a big loss.
close out the account.” “You have to recognize that there is unlimited po-
Instead, Mr. O™Connor, the 46-year-old owner of a tential for disaster” in selling naked options, says Peter
small medical X-ray printing concern in Grand Rapids, Thayer, executive vice president of Gateway Investment
Michigan, got caught in one of the worst investor Advisors Inc., a Cincinnati-based investment firm that
blowouts in history. In a few minutes on October trades options to hedge its stock portfolios. Last Sep-
19, he lost everything in his account plus an addi- tember, Gateway bought out-of-the-money put options
tional $91,000”a total loss of 175% of his original on the S&P 100 stock index on the CBOE at $2 to $3 a
investment. contract as “insurance” against a plunging market. By
October 20, the day after the crash, the value of those
contracts had soared to $130. Although Gateway prof-
SCENE OF DISASTER
ited handsomely, the parties on the other side of the
For Mr. O™Connor and hundreds of other investors, a trade were clobbered.
little-known corner of the Chicago Board Options Ex-
change was the “black hole” of Black Monday™s market
FIRM SUED
crash. In a strategy marketed by brokers nationwide as
a sure thing, these customers had sunk hundreds of Brokers who were pushing naked options assumed that
millions of dollars into “naked puts””unhedged, highly the stock market wouldn™t plunge into uncharted terri-
leveraged bets that the stock market was in no danger tory. Frank VanderHoff, one of the two main brokers

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