Futures and option

Mechanics of
Options Markets

We introduced options in Chapter 1. This chapter explains how options markets are
organized, what terminology is used, how the contracts are traded, how margin
requirements are set, and so on. Later chapters will examine such topics as trading
strategies involving options, the determination of option prices, and the ways in which
portfolios of options can be hedged. This chapter is concerned primarily with stock
options. It presents some introductory material on currency options, index options, and
futures options. More details concerning these instruments can be found in Chapters 16
and 17.

Options are fundamentally different from forward and futures contracts. An option
gives the holder of the option the right to do something, but the holder does not have to
exercise this right. By contrast, in a forward or futures contract, the two parties have
committed themselves to some action. It costs a trader nothing (except for the margin
requirements) to enter into a forward or futures contract, whereas the purchase of an
option requires an up-front payment.

When charts showing the gain or loss from options trading are produced, the usual
practice is to ignore discounting, so that the profit is the final payoff minus the initial
cost. This chapter follows this practice.

9.1 TYPES OF OPTIONS

As mentioned in Chapter 1, there are two basic types of options. A call option gives the
holder of the option the right to buy an asset by a certain date for a certain price. A put
option gives the holder the right to sell an asset by a certain date for a certain price. The
date specified in the contract is known as the expiration date or the maturity date.
The price specified in the contract is known as the exercise price or the strike price.

Options can be either American or European, a distinction that has nothing to do
with geographical location. American options can be exercised at any time up to the
expiration date, whereas European options can be exercised only on the expiration date
itself. Most of the options that are traded on exchanges are American. However,
European options are generally easier to analyze than American options, and some
of the properties of an American option are frequently deduced from those of its
European counterpart.

194

9C H A P T E R

Call Options

Consider the situation of an investor who buys a European call option with a strike
price of $100 to purchase 100 shares of a certain stock. Suppose that the current stock
price is $98, the expiration date of the option is in 4 months, and the price of an option
to purchase one share is $5. The initial investment is $500. Because the option is
European, the investor can exercise only on the expiration date. If the stock price on this
date is less than $100, the investor will clearly choose not to exercise. (There is no point
in buying for $100 a share that has a market value of less than $100.) In these
circumstances, the investor loses the whole of the initial investment of $500. If the
stock price is above $100 on the expiration date, the option will be exercised. Suppose,
for example, that the stock price is $115. By exercising the option, the investor is able to
buy 100 shares for $100 per share. If the shares are sold immediately, the investor makes
a gain of $15 per share, or $1,500, ignoring transactions costs. When the initial cost of
the option is taken into account, the net profit to the investor is $1,000.

Figure 9.1 shows how the investor’s net profit or loss on an option to purchase one
share varies with the final stock price in the example. It is important to realize that an
investor sometimes exercises an option and makes a loss overall. Suppose that, in the
example, the stock price is $102 at the expiration of the option. The investor would
exercise the option contract for a gain of 100�ð$102�$100Þ ¼ $200 and realize a loss
overall of $300 when the initial cost of the option is taken into account. It is tempting to
argue that the investor should not exercise the option in these circumstances. However,
not exercising would lead to an overall loss of $500, which is worse than the $300 loss
when the investor exercises. In general, call options should always be exercised at the
expiration date if the stock price is above the strike price.

Put Options

Whereas the purchaser of a call option is hoping that the stock price will increase, the
purchaser of a put option is hoping that it will decrease. Consider an investor who
buys a European put option with a strike price of $70 to sell 100 shares of a certain

Profit ($)

Terminal
stock price ($)

130120110100908070

−5

0

10

20

30

Figure 9.1 Profit from buying a European call option on one share of a stock. Option
price ¼ $5; strike price ¼ $100.

Mechanics of Options Markets 195

stock. Suppose that the current stock price is $65, the expiration date of the option is

in 3 months, and the price of an option to sell one share is $7. The initial investment is

$700. Because the option is European, it will be exercised only if the stock price is
below $70 on the expiration date. Suppose that the stock price is $55 on this date. The

investor can buy 100 shares for $55 per share and, under the terms of the put option,

sell the same shares for $70 to realize a gain of $15 per share, or $1,500. (Again,
transactions costs are ignored.) When the $700 initial cost of the option is taken into

account, the investor’s net profit is $800. There is no guarantee that the investor will

make a gain. If the final stock price is above $70, the put option expires worthless, and

the investor loses $700. Figure 9.2 shows the way in which the investor’s profit or loss
on an option to sell one share varies with the terminal stock price in this example.

Early Exercise

As already mentioned, exchange-traded stock options are generally American rather

than European. This means that the investor in the foregoing examples would not have to

wait until the expiration date before exercising the option. We will see in later chapters
that there are some circumstances when it is optimal to exercise American options before

the expiration date.

9.2 OPTION POSITIONS

There are two sides to every option contract. On one side is the investor who has taken

the long position (i.e., has bought the option). On the other side is the investor who has

taken a short position (i.e., has sold or written the option). The writer of an option

receives cash up front, but has potential liabilities later. The writer’s profit or loss is the
reverse of that for the purchaser of the option. Figures 9.3 and 9.4 show the variation of

the profit or loss with the final stock price for writers of the options considered in

Figures 9.1 and 9.2.

Profit ($)

Terminal
stock price ($)

100908070605040

−7

0

10

20

30

Figure 9.2 Profit from buying a European put option on one share of a stock. Option
price ¼ $7; strike price = $70.

196 CHAPTER 9

There are four types of option positions:

1. A long position in a call option

2. A long position in a put option

3. A short position in a call option

4. A short position in a put option.

It is often useful to characterize a European option in terms of its payoff to the
purchaser of the option. The initial cost of the option is then not included in the

calculation. If K is the strike price and ST is the final price of the underlying asset, the

Profit ($)

Terminal
stock price ($)

130120110

100908070

−10

0

5

−20

−30

Figure 9.3 Profit from writing a European call option on one share of a stock. Option
price ¼ $5; strike price ¼ $100.

Profit ($)

Terminal
stock price ($)

70

605040

1009080

−10

0

7

−20

−30

Figure 9.4 Profit from writing a European put option on one share of a stock. Option
price ¼ $7; strike price ¼ $70.

Mechanics of Options Markets 197

payoff from a long position in a European call option is

maxðST � K; 0Þ

This reflects the fact that the option will be exercised if ST > K and will not be exercised
if ST 6 K. The payoff to the holder of a short position in the European call option is

�maxðST � K; 0Þ ¼ minðK � ST; 0Þ

The payoff to the holder of a long position in a European put option is

maxðK � ST; 0Þ

and the payoff from a short position in a European put option is

�maxðK � ST; 0Þ ¼ minðST � K; 0Þ

Figure 9.5 illustrates these payoffs.

9.3 UNDERLYING ASSETS

This section provides a first look at options on stocks, currencies, stock indices, and
futures.

Payoff

(a)

ST

K

Payoff

(b)

ST

K

Payoff

(c)

ST

K

Payoff

(d)

ST

K

Figure 9.5 Payoffs from positions in European options: (a) long call; (b) short call;
(c) long put; (d) short put. Strike price ¼ K; price of asset at maturity ¼ ST .

198 CHAPTER 9

Stock Options

Most trading in stock options is on exchanges. In the United States, the exchanges
include the Chicago Board Options Exchange (www.cboe.com), NASDAQ OMX
(www.nasdaqtrader.com), which acquired the Philadelphia Stock Exchange in 2008,
NYSE Euronext (www.euronext.com), which acquired the American Stock Exchange
in 2008, the International Securities Exchange (www.iseoptions.com), and the Boston
Options Exchange (www.bostonoptions.com). Options trade on more than 2,500
different stocks. One contract gives the holder the right to buy or sell 100 shares at
the specified strike price. This contract size is convenient because the shares themselves
are normally traded in lots of 100.

Foreign Currency Options

Most currency options trading is now in the over-the-counter market, but there is some
exchange trading. Exchanges trading foreign currency options in the United States
include NASDAQ OMX. This exchange offers European-style contracts on a variety of
different currencies. One contract is to buy or sell 10,000 units of a foreign currency
(1,000,000 units in the case of the Japanese yen) for US dollars. Foreign currency
options contracts are discussed further in Chapter 16.

Index Options

Many different index options currently trade throughout the world in both the over-the-
counter market and the exchange-traded market. The most popular exchange-traded
contracts in the United States are those on the S&P 500 Index (SPX), the S&P 100 Index
(OEX), the Nasdaq-100 Index (NDX), and the Dow Jones Industrial Index (DJX). All
of these trade on the Chicago Board Options Exchange. Most of the contracts are
European. An exception is the OEX contract on the S&P 100, which is American. One
contract is usually to buy or sell 100 times the index at the specified strike price.
Settlement is always in cash, rather than by delivering the portfolio underlying the
index. Consider, for example, one call contract on an index with a strike price of 980. If
it is exercised when the value of the index is 992, the writer of the contract pays the
holder ð992�980Þ�100 ¼ $1,200. Index options are discussed further in Chapter 16.

Futures Options

When an exchange trades a particular futures contract, it often also trades options on
that contract. A futures option normally matures just before the delivery period in the
futures contract. When a call option is exercised, the holder’s gain equals the excess of
the futures price over the strike price. When a put option is exercised, the holder’s gain
equals the excess of the strike price over the futures price. Futures options contracts are
discussed further in Chapter 17.

9.4 SPECIFICATION OF STOCK OPTIONS

In the rest of this chapter, we will focus on stock options. As already mentioned, an
exchange-traded stock option in the United States is an American-style option contract

Mechanics of Options Markets 199

to buy or sell 100 shares of the stock. Details of the contract (the expiration date, the

strike price, what happens when dividends are declared, how large a position investors

can hold, and so on) are specified by the exchange.

Expiration Dates

One of the items used to describe a stock option is the month in which the expiration

date occurs. Thus, a January call trading on IBM is a call option on IBM with an

expiration date in January. The precise expiration date is the Saturday immediately

following the third Friday of the expiration month. The last day on which options trade

is the third Friday of the expiration month. An investor with a long position in an

option normally has until 4:30 p.m. Central Time on that Friday to instruct a broker to

exercise the option. The broker then has until 10:59 p.m. the next day to complete the

paperwork notifying the exchange that exercise is to take place.

Stock options in the United States are on a January, February, or March cycle. The

January cycle consists of the months of January, April, July, and October. The

February cycle consists of the months of February, May, August, and November.

The March cycle consists of the months of March, June, September, and December.

If the expiration date for the current month has not yet been reached, options trade with

expiration dates in the current month, the following month, and the next two months in

the cycle. If the expiration date of the current month has passed, options trade with

expiration dates in the next month, the next-but-one month, and the next two months

of the expiration cycle. For example, IBM is on a January cycle. At the beginning of

January, options are traded with expiration dates in January, February, April, and July;

at the end of January, they are traded with expiration dates in February, March, April,

and July; at the beginning of May, they are traded with expiration dates in May, June,

July, and October; and so on. When one option reaches expiration, trading in another is

started. Longer-term options, known as LEAPS (long-term equity anticipation secu-

rities), also trade on about 800 stocks in the United States. These have expiration dates

up to 39 months into the future. The expiration dates for LEAPS on stocks are always

in January.

Strike Prices

The exchange normally chooses the strike prices at which options can be written so that

they are spaced $2.50, $5, or $10 apart. Typically the spacing is $2.50 when the stock

price is between $5 and $25, $5 when the stock price is between $25 and $200, and

$10 for stock prices above $200. As will be explained shortly, stock splits and stock

dividends can lead to nonstandard strike prices.

When a new expiration date is introduced, the two or three strike prices closest to the

current stock price are usually selected by the exchange. If the stock price moves outside

the range defined by the highest and lowest strike price, trading is usually introduced in

an option with a new strike price. To illustrate these rules, suppose that the stock price

is $84 when trading begins in the October options. Call and put options would

probably first be offered with strike prices of $80, $85, and $90. If the stock price rose

above $90, it is likely that a strike price of $95 would be offered; if it fell below $80, it is

likely that a strike price of $75 would be offered; and so on.

200 CHAPTER 9

Terminology

For any given asset at any given time, many different option contracts may be trading.
Consider a stock that has four expiration dates and five strike prices. If call and put
options trade with every expiration date and every strike price, there are a total of
40 different contracts. All options of the same type (calls or puts) are referred to as an
option class. For example, IBM calls are one class, whereas IBM puts are another class.
An option series consists of all the options of a given class with the same expiration date
and strike price. In other words, an option series refers to a particular contract that is
traded. For example, IBM 70 October calls would constitute an option series.

Options are referred to as in the money, at the money, or out of the money. If S is the
stock price and K is the strike price, a call option is in the money when S > K, at the
money when S ¼ K, and out of the money when S < K. A put option is in the money
when S < K, at the money when S ¼ K, and out of the money when S > K. Clearly, an
option will be exercised only when it is in the money. In the absence of transactions
costs, an in-the-money option will always be exercised on the expiration date if it has
not been exercised previously.

The intrinsic value of an option is defined as the maximum of zero and the value the
option would have if it were exercised immediately. For a call option, the intrinsic value
is therefore maxðS � K; 0Þ. For a put option, it is maxðK � S; 0Þ. An in-the-money
American option must be worth at least as much as its intrinsic value because the
holder can realize the intrinsic value by exercising immediately. Often it is optimal for
the holder of an in-the-money American option to wait rather than exercise immedi-
ately. The option is then said to have time value. The total value of an option can be
thought of as the sum of its intrinsic value and its time value.

FLEX Options

The Chicago Board Options Exchange offers FLEX (short for flexible) options on
equities and equity indices. These are options where the traders on the floor of the
exchange agree to nonstandard terms. These nonstandard terms can involve a strike
price or an expiration date that is different from what is usually offered by the exchange.
It can also involve the option being European rather than American. FLEX options are
an attempt by option exchanges to regain business from the over-the-counter markets.
The exchange specifies a minimum size (e.g., 100 contracts) for FLEX option trades.

Dividends and Stock Splits

The early over-the-counter options were dividend protected. If a company declared a
cash dividend, the strike price for options on the company’s stock was reduced on the
ex-dividend day by the amount of the dividend. Exchange-traded options are not
usually adjusted for cash dividends. In other words, when a cash dividend occurs,
there are no adjustments to the terms of the option contract. An exception is sometimes
made for large cash dividends (see Snapshot 9.1).

Exchange-traded options are adjusted for stock splits. A stock split occurs when the
existing shares are ‘‘split’’ into more shares. For example, in a 3-for-1 stock split, three
new shares are issued to replace each existing share. Because a stock split does not
change the assets or the earning ability of a company, we should not expect it to have

Mechanics of Options Markets 201

any effect on the wealth of the company’s shareholders. All else being equal, the 3-for-1
stock split should cause the stock price to go down to one-third of its previous value. In
general, an n-for-m stock split should cause the stock price to go down to m=n of its
previous value. The terms of option contracts are adjusted to reflect expected changes in
a stock price arising from a stock split. After an n-for-m stock split, the strike price is
reduced to m=n of its previous value, and the number of shares covered by one contract
is increased to n=m of its previous value. If the stock price declines in the way expected,
the positions of both the writer and the purchaser of a contract remain unchanged.

Example 9.1

Consider a call option to buy 100 shares of a company for $30 per share. Suppose
the company makes a 2-for-1 stock split. The terms of the option contract are then
changed so that it gives the holder the right to purchase 200 shares for $15 per share.

Stock options are adjusted for stock dividends. A stock dividend involves a company
issuing more shares to its existing shareholders. For example, a 20% stock dividend
means that investors receive one new share for each five already owned. A stock
dividend, like a stock split, has no effect on either the assets or the earning power of
a company. The stock price can be expected to go down as a result of a stock dividend.
The 20% stock dividend referred to is essentially the same as a 6-for-5 stock split. All
else being equal, it should cause the stock price to decline to 5/6 of its previous value.
The terms of an option are adjusted to reflect the expected price decline arising from a
stock dividend in the same way as they are for that arising from a stock split.

Example 9.2

Consider a put option to sell 100 shares of a company for $15 per share. Suppose
the company declares a 25% stock dividend. This is equivalent to a 5-for-4 stock
split. The terms of the option contract are changed so that it gives the holder the
right to sell 125 shares for $12.

Snapshot 9.1 Gucci Group’s Large Dividend

When there is a large cash dividend (typically one that is more than 10% of the stock
price), a committee of the Options Clearing Corporation (OCC) at the Chicago Board
Options Exchange can decide to adjust the terms of options traded on the exchange.

On May 28, 2003, Gucci Group NV (GUC) declared a cash dividend of 13.50 euros
(approximately $15.88) per common share and this was approved at the annual
shareholders’ meeting on July 16, 2003. The dividend was about 16% of the share
price at the time it was declared. In this case, the OCC committee decided to adjust the
terms of options. The result was that the holder of a call contract paid 100 times the
strike price on exercise and received $1,588 of cash in addition to 100 shares; the holder
of a put contract received 100 times the strike price on exercise and delivered $1,588 of
cash in addition to 100 shares. These adjustments had the effect of reducing the strike
price by $15.88.

Adjustments for large dividends are not always made. For example, Deutsche
Terminbörse chose not to adjust the terms of options traded on that exchange when
Daimler-Benz surprised the market on March 10, 1998, with a dividend equal to about
12% of its stock price.

202 CHAPTER 9

Adjustments are also made for rights issues. The basic procedure is to calculate the

theoretical price of the rights and then to reduce the strike price by this amount.

Position Limits and Exercise Limits

The Chicago Board Options Exchange often specifies a position limit for option con-

tracts. This defines the maximum number of option contracts that an investor can hold on

one side of the market. For this purpose, long calls and short puts are considered to be on

the same side of the market. Also considered to be on the same side are short calls and

long puts. The exercise limit usually equals the position limit. It defines the maximum

number of contracts that can be exercised by any individual (or group of individuals

acting together) in any period of five consecutive business days. Options on the largest

and most frequently traded stocks have positions limits of 250,000 contracts. Smaller

capitalization stocks have position limits of 200,000, 75,000, 50,000, or 25,000 contracts.

Position limits and exercise limits are designed to prevent the market from being

unduly influenced by the activities of an individual investor or group of investors.

However, whether the limits are really necessary is a controversial issue.

9.5 TRADING

Traditionally, exchanges have had to provide a large open area for individuals to meet

and trade options. This has changed. Most derivatives exchanges are fully electronic,

so traders do not have to physically meet. The International Securities Exchange

(www.iseoptions.com) launched the first all-electronic options market for equities in

the United States in May 2000. Over 95% of the orders at the Chicago Board Options

Exchange are handled electronically. The remainder are mostly large or complex

institutional orders that require the skills of traders.

Market Makers

Most options exchanges use market makers to facilitate trading. A market maker for a

certain option is an individual who, when asked to do so, will quote both a bid and

an offer price on the option. The bid is the price at which the market maker is

prepared to buy, and the offer or asked is the price at which the market maker is

prepared to sell. At the time the bid and offer prices are quoted, the market maker

does not know whether the trader who asked for the quotes wants to buy or sell the

option. The offer is always higher than the bid, and the amount by which the offer

exceeds the bid is referred to as the bid–offer spread. The exchange sets upper limits

for the bid–offer spread. For example, it might specify that the spread be no more

than $0.25 for options priced at less than $0.50, $0.50 for options priced between

$0.50 and $10, $0.75 for options priced between $10 and $20, and $1 for options

priced over $20.

The existence of the market maker ensures that buy and sell orders can always be

executed at some price without any delays. Market makers therefore add liquidity to the

market. The market makers themselves make their profits from the bid–offer spread.

They use methods such as those that will be discussed in Chapter 18 to hedge their risks.

Mechanics of Options Markets 203

Offsetting Orders

An investor who has purchased options can close out the position by issuing an

offsetting order to sell the same number of options. Similarly, an investor who has

written options can close out the position by issuing an offsetting order to buy the same

number of options. (In this respect options markets are similar to futures markets.) If,

when an option contract is traded, neither investor is closing an existing position, the

open interest increases by one contract. If one investor is closing an existing position

and the other is not, the open interest stays the same. If both investors are closing

existing positions, the open interest goes down by one contract.

9.6 COMMISSIONS

The types of orders that can be placed with a broker for options trading are similar to

those for futures trading (see Section 2.8). A market order is executed immediately, a limit

order specifies the least favorable price at which the order can be executed, and so on.

For a retail investor, commissions vary significantly from broker to broker. Discount

brokers generally charge lower commissions than full-service brokers. The actual

amount charged is often calculated as a fixed cost plus a proportion of the dollar

amount of the trade. Table 9.1 shows the sort of schedule that might be offered by a

discount broker. Using this schedule, the purchase of eight contracts when the option

price is $3 would cost $20þð0:02�$2,400Þ ¼ $68 in commissions.
If an option position is closed out by entering into an offsetting trade, the commis-

sion must be paid again. If the option is exercised, the commission is the same as it

would be if the investor placed an order to buy or sell the underlying stock.

Consider an investor who buys one call contract with a strike price of $50 when the

stock price is $49. We suppose the option price is $4.50, so that the cost of the contract

is $450. Under the schedule in Table 9.1, the purchase or sale of one contract always

costs $30 (both the maximum and minimum commission is $30 for the first contract).

Suppose that the stock price rises and the option is exercised when the stock reaches

$60. Assuming that the investor pays 0.75% commission to exercise the option and a

further 0.75% commission to sell the stock, there is an additional cost of

2�0:0075�$60�100 ¼ $90

Table 9.1 A typical commission schedule for a discount broker.

Dollar amount of trade Commission�

<$2,500 $20 þ 2% of dollar amount $2,500 to $10,000 $45 þ 1% of dollar amount >$10,000 $120 þ 0.25% of dollar amount

� Maximum commission is $30 per contract for the first five contracts plus
$20 per contract for each additional contract. Minimum commission is $30
per contract for the first contract plus $2 per contract for each additional
contract.

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