endar spread, for example,
one could see what sorts of profitability he would be looking at when it was time to
remove the spread.
Chapter 28: Mathematical Applications 487
Finally, the computer can compute the expected return of a position already in
place. This would give a more dynamic picture of the position, and this expected
return is usually for a relatively short time period. That time period might be 30 days,
or the time remaining until expiration, whichever is less. The expected return is cal
culated in much the same manner as the expected return computation described ear
lier in this chapter. First, one uses the stock's volatility to construct a range of prices
over which to examine the position. Second, one uses the Black-Scholes model to
calculate the values of the various options in the position at that future time and at
the various stock prices. Some of the results should be displayed in table form by the
computer program. The expected profit is computed, as described earlier, by sum
ming the multiples of the probabilities of the stock being at each price by the result
of the position at that price. The expected return is then computed by dividing the
expected profit by the expected investment. Since margin computations can require
involved computer programs, it is sufficient to omit this last step and merely observe
the expected profit. The following example shows how a sample position might look
as the computer displays the position itself, the ESP, the profit at expiration, and the
expected profit in 30 days. A complex position is assumed, in order that the value of
these analyses can be demonstrated.
Example: The following position exists when XYZ is at 31 ¾. It is essentially a back
spread combined with a reverse ratio write. It resembles a long straddle in that there
is increased profit potential in either direction if the stock moves far enough by expi
ration. Initially, the computer should display the position and the ESP.
Position Delta ESP
Short 4,500 XYZ 1.00 Short 4,500 shares
Short 100 XYZ April 25 calls 0.89 Short 8, 900 shares
Long 50 XYZ April 30 calls 0.76 Long 3,800 shares
Long 139 XYZ July 30 calls 0.74 Long 10,286 shares
Total ESP Long 686 shares
Total money in position: $163,500 credit
The advantage of using the ESP is that this fairly complex position is reduced to a sin
gle number. The entire position is equivalent to being long 686 shares of the com
mon stock. Essentially, this is close to delta-neutral for such a large position. The next
item that the computer should display is the total credit or debit in the position to
date. With this information, an expiration picture can be drawn if it is applicable. In
this position, since there is a mixture of April and July options, a strict expiration pie-
488 Part IV: Additional Considerations
ture does not apply. Rather, the computer should draw a picture based on the posi
tion at April expiration or on a shorter time horizon.
Assume that April expiration is still some time away, so that the computer will
instead draw the picture 30 days hence. In order to do so, the computer uses the
stock's volatility to project stock prices 30 days in the future. Seven stock prices are
shown in the next table; they represent points along the distribution curve of the
stock, ranging from minus one and one-half standard deviations to plus one and one
half standard deviations of movement from the current stock price. While these
seven points certainly do not comprise the entire spectrum of possible stock moves,
they are a representative sample.
Stock Price Standard Expected
in 30 Days Deviations Results
353/a + 1.5 +$15,847
34 1/a +1.0 + 12,355
327/a +0.5 + 10,097
31 3/4 0.0 + 9,443
305/a -0.5 + 10,743
291/2 -1.0 + 14,172
281/2 -1.5 + 19,605
Expected profit +$11,426
Obviously, this position has had some profitable adjustments made to it in the past.
That is not important at this point, because the trader is interested only in the future.
If the current mark to market of this position were in excess of $11,426, then he
should consider removing the position, since it would be more profitable than the
expected profit.
IMPLEMENTATION
Many of the analyses described in this chapter can be obtained from a reliable data
service or brokerage firm. The strategist who plans to prepare his own analysis, either
by himself or by contracting the programming work out, should be aware that com
puter programs cannot be written in the COBOL language, because the mathemat
ics are far too complicated for a business language. Languages such as Pascal, C,
C++, Visual Basic, or any high-level structured programming language would suffice,
although Java could be considered as well, keeping in mind that Java's main usage is
not for computational purposes. Reliable option pricing data that include dividend
Chapter 28: Mathematical Applications 489
information on the underlying stock are also necessary. The larger programmable cal
culators can handle calculations such as the Black-Scholes model, computing the
hedge ratio, and determining the probability of a stock being above or below a cer
tain price at some future time. However, more involved calculations, such as com
puting the implied volatility or determining the expected return of a position, require
the use of a computer.
SUMMARY
Two basic mathematical aids have been presented: the pricing model and the ability
to predict the probability of a stock's movement. The hedge ratio and the expected
return analysis are extensions of the basic aids. Any strategy can be evaluated with
these tools. Such an analysis should be able to give the trader or strategist some idea
of the relative attractiveness of establishing the position, and may also aid in making
follow-up adjustments to the position. All the analyses rely heavily on one's estimate
of the volatility of the underlying stock Using the implied volatility seems to be one


basic aids. Any strategy can be evaluated with
these tools. Such an analysis should be able to give the trader or strategist some idea
of the relative attractiveness of establishing the position, and may also aid in making
follow-up adjustments to the position. All the analyses rely heavily on one's estimate
of the volatility of the underlying stock Using the implied volatility seems to be one
of the best ways to obtain an accurate, current volatility estimate, since it is derived
from the prices in the market itself. The applications presented here are not all-inclu
sive. The strategist who is, or becomes, familiar with the advantages of rigorous math
ematical analysis will be able to construct many other aids for his trading that utilize
the basic mathematics described in this chapter.

Introduction to Index Option
Products and Futures
Since their introduction in 1981, listed index options have proved to be very popular.
Index options are options whose underlying security is not a single stock but rather an
index composed of many stocks. These include options on index futures contracts.
Most popular types of cash settlement options are options on indices or subindices. The
strategies employed in trading these options are not substantially different from those
used in trading stock options, with a few notable exceptions. However, the options
themselves tend to be priced differently and to trade differently. It is these differences
between stock options and index options on which we will predominantly concentrate.
Index products - cash-based options, futures-based options, and index futures -
will be the main topic of discussion in this section of the book. We will look at how
indices are constructed, how to use these products to speculate, how to hedge, and
how to spread one index against another. Both futures and options will be used in
these strategies. The discussion of other futures options - currencies, grains, bonds,
etc - will be deferred to a later chapter.
In this chapter, we will be looking at introductory facts about index options and
futures which differentiate them from the equity options that have encompassed the
entire previous part of this book. First, however, we will take an in-depth look at stock
indices and the methods of calculating them. Also in this chapter there will be a dis
cussion of futures contracts and how trading them differs from trading stocks and
stock options.
INDICES
Since many cash-based or futures options have an index of stocks underlying the
option, it is useful to understand how indices are calculated, in order that one may
be able to understand how an individual stock's movement within the index affects
493
494 Part V: Index Options and Futures
the overall value of the index. The indices on which options are traded are generally
stock indices - that is, the items making up the index are stocks. There are two main
ways of calculating a stock index: weighted by price or weighted by capital.
CAPITALIZATION-WEIGHTED INDICES
The capitalization of a stock is the total dollar value of its securities to current mar
ket prices: It is the multiple of the number of shares outstanding (the float) and the
current stock price. In a capitalization-weighted index, the capitalizations of all stocks
in the index are computed and added together to produce the total market value of
the index. The price of each stock in the index is multiplied by the total number of
shares of that stock that are outstanding (the "float"), and their sum is calculated.
Finally, this total sum is divided by another number, termed the "divisor," to produce
the final index value. An example will help to illustrate the concept of calculating the
value of a capitalization-weighted index.
Example: Suppose that an index is composed of three stocks whose prices and floats
are given in the following table. The multiple of price times float ( capitalization) is
also included in the table.
Stock Price Float Capitalization
A 30 175,000,000 5,250,000000
B 90 50,000,000 4,500,000,000
C 50 100,000,000 5,000,000,000
Total capitalization: 14,750,000,000
Most indices use a divisor since it would be unwieldy to say that the index closed at
14,750,000,000 (for example, think of trying to quote the Dow-Jones Industrial
Average as such a large figure). The divisor is generally an arbitrary number that is
initially used to reduce the index value to a workable number. When an index is ini
tiated, the divisor might be set so that the index starts out at an even number.
Suppose that in the sample index above, we wanted the initial value - as represent
ed by the given prices and floats - to be 100.00. Then we would set the initial divisor
to 147,500,000. Thus the total capitalization of the index divided by the divisor would
give a value of 100.00.
The divisor of an index can be changed to provide continuity for the index's
value when changes occur in the individual components. Note that the divisor does
not have to be changed when a stock splits, because the price is adjusted downward
automatically by an amount equal to the increase in the float of the stock that is split
ting. Notice that in the above example, if stock B should split 2-for-l then its price
Chapter 29: Introduction to Index Option Products and Futures 495
would be 45 (90 + 2) and its float would double to 100 million shares from 50 mil
lion. Thus, the capitalization of stock B remains the same: $4,500,000,000.
However, if a stock should alter its capitalization in a manner that is not reflect
ed by an automatic adjustment in its price, then the divisor must be changed. For
example, a company might issue more stock in a secondary offering - something that
would not cause the exchange where the stock is listed to automatically reduce the
price of the stock. To produce continuity in the value of the index between the day
the secondary is issued and the day after it is issued,

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reflect
ed by an automatic adjustment in its price, then the divisor must be changed. For
example, a company might issue more stock in a secondary offering - something that
would not cause the exchange where the stock is listed to automatically reduce the
price of the stock. To produce continuity in the value of the index between the day
the secondary is issued and the day after it is issued, the divisor is changed to keep
the index value the same. Consider the following example.
Example: Using the same sample index as before, suppose that the following prices
exist at the closing one day:
Stock Price Float Capitalization
A 40 175,000,000 7, 000000000
B 80 50,000,000 4,000,000,000
C 60 100,000,000 6,000,000,000
Total capitalization: 17,000,000,000
Divisor: 147,500,000
Index value: 115.25
Now suppose that stock A issues a 2-million-share secondary that evening, giving that
stock a total float of 177 million shares. Such an action would change the value of the
index as follows:
Stock Price Float Capitalization
A 40 177,000,000 7,080,000,000
B 80 50,000,000 4,000,000,000
C 60 100,000,000 6,000,000,000
Total capitalization: 17,080,000,000
Divisor: 147,500,000
Index value: 115.80
However, it makes no sense to change the value of the index from 115.25 to 115.80
when nothing actually changed in the marketplace. If investors deem it necessary to
lower the price of stock A in the marketplace because of the secondary issue, so be
it. But such a change in investor philosophy would be reflected in the price of the
index as the stock drops. So, in order to keep the value of the index the same on the
morning after the secondary is issued, the divisor must be changed to reflect the extra
2 million shares of stock A. The new divisor would be equal to the new total capital-
496 Part V: Index Options and Futures
ization (17,080,000,000) divided by the old index value (115.2542373). This would
give the new divisor:
New divisor: 148,194,117.6
As this example demonstrates, the divisor of a capitalization-weighted index can
change quite often. Fortunately, there are organizations that are responsible for
keeping the index current and for calculating the divisor every time it needs chang
ing. Thus, an investor who needs to know the latest divisor can generally find it out
by making a phone call or visiting a Web site. This is far easier than keeping track of
everything by oneself.
In a capitalization-weighted index, the stocks with the largest market value have
the most weight within the index. This means that indices that contain such largely
capitalized stocks as IBM, AT&T, General Electric, Exxon, and General Motors will
be dominated by those stocks. For example, the S&P 500 is one of the largest capi
talization-weighted indices in terms of the number of stocks (500). However, IBM
has such a large capitalization that it accounts for over 5% of the index. Obviously,
there are many stocks in the S&P 500 that do not really have much weight at all. In
order to compute the percentage that a stock comprises of the index, it is merely nec
essary to divide that stock's capitalization by the total capitalization of the index.
Using the previous example, one can see how the percentage is computed.
Stock Price Float Capitalization Pct
A 40 1 77,000,000 7,080,000,000 41.5%
B 80 50,000,000 4,000,000,000 23.4%
C 60 100,000,000 6,000,000,000 35.1%
Total capitalization: 17,080,000,000 100.0%
Another interesting statistic to know regarding any index is how many shares of
each stock are in the index. In a capitalization-weighted index, the number of shares
of each stock is determined by dividing the stock's float by the divisor of the index. In
the same sample index, the following table shows how many shares of each stock are
in the index.
Stock Price Float Capitalization Shares
A 40 177,000,000 7,080,000,000 1.20
B 80 50,000,000 4,000,000,000 0.34
C 60 100,000,000 6,000,000,000 0.68
Total capitalization: 17,080,000,000
Divisor: 147,500,000
Index value: 115 .80
Chapter 29: Introduction to Index Option Products and Futures 497
Thus, if stock A goes up by one point, then the value of the index would increase
by 1.20 points since there are 1.2 shares of stock A in the index. One can see the value
of computing such a statistic - it readily allows him to see how any individual stock's
movement will affect the index movement during a trading day. This is especially use
ful when a stock is halted, but the index itself keeps trading.
Example: Suppose that, in the above index, stock Chas halted trading. There are
0.68 shares of stock C in the index. Suppose that stock C is indicated 3 points lower,
but that the index is currently trading unchanged from the previous night's close due
to the fact that both stocks A and B are unchanged on the day. If one were to try to
price the options on the index, he would be wrong to use the current price of the
index since that will soon change when stock C opens. However, there is not really a
problem since one can readily see that if stock C opens 3 points lower, then the index
will drop by 2.04 points (3 x 0.68). Thus one should price the options as if the index
were already trading about 2 points lower. This kind of anticipation depends, of
course, on knowing the number of shares of stock C in the index.
A similar type of analysis is useful when trying to predict longer-term effects of
a stock on an index. If you thought stock C had a chance of rallying 30 points, then
one can see that this would cause the index to rise over 20 points. Given this type of
relationship, there are sometimes option spreads between the stock's options and the
index's options that will be profitable based on such an assumption.
It should also be noted that the number of shares of stock in a capitalization
weighted index does not change on a daily basis since it does not depend on the price
of the stocks in the index. However, the pe


ver 20 points. Given this type of
relationship, there are sometimes option spreads between the stock's options and the
index's options that will be profitable based on such an assumption.
It should also be noted that the number of shares of stock in a capitalization
weighted index does not change on a daily basis since it does not depend on the price
of the stocks in the index. However, the percent that each stock comprises of the index
does change each day as prices change. Thus, the number of shares is a more stable
statistic to keep track of, and is also more directly usable to anticipate index value
changes as stock prices change.
Capitalization-weighted indices are the most prevalent type, and most investors
are familiar with several of them: the Standard and Poor's 500, the Standard and
Poor's 400, the Standard and Poor's 100 (also called by its quote symbol, OEX), the
New York Stock Exchange Index, and the American Stock Exchange Index.
PRICE-WEIGHTED INDICES
A price-weighted index contains an equal number of shares of each stock in the index.
A price-weighted index is computed by adding together the prices of the various
stocks in the index and then dividing that sum by the divisor to produce the index
value. Again, the divisor is initially an arbitrary number that is used to produce a
desired original index value-something like 100.00, for example. Let us use the same
498 Part V: Index Options and Futures
three stocks we were using above to construct an example of a price-weighted index.
Assume the divisor at the time of this example is 1.65843.
Stock
A
B
C
Price total:
Divisor: 1.65843
Index value: 102.51
Price
30
90
50
170
Unlike the capitalization-weighted index, the divisor needs to be changed when
a stock's price is adjusted by the exchange where it is listed (as in a stock split or stock
dividend) but does not have to be adjusted when the company issues more stock.
That is, the divisor in a price-weighted index is changed when the price of the stock
is adjusted, but not when the stock's capitalization is changed.
If a certain stock issues new stock in a secondary offering, the exchange where
its stock is listed will not automatically adjust the price of the stock downward.
Hence, there is no change to the divisor of any price-weighted index containing that
stock because the closing price of the stock was not adjusted by the exchange.
However, in the above example, if stock B should split 2-for-l, the exchange
would change its closing from 90 to 45. Thus, the sum of the stocks in the price
weighted index would change without the market even being open. Consequently,
the divisor would need to be changed to reflect the split. The following example sums
up the situation after stock B splits 2-for-l.
Stock
A
B
C
Price total:
Old divisor: 1 .65843
Price
30
45
50
125
Previous closing index value: 102.51
New divisor (i.e., the divisor necessary to keep the index
value unchanged): 1 .21943
The new divisor is calculated by dividing the new sum of the prices, 125, by the
old closing price, 102.51. Thus the divisor is reduced in order to produce the same
index value - 102.51 - even though the sum of the prices of the stocks in the index
is now 125 instead of the previous 170. Note that the new divisor is not dependent
on the old divisor.
Chapter 29: Introduction to Index Option Products and Futures 499
Another statistic that we looked at with capitalization-weighted indices was the
number of shares of each stock in the index. In a price-weighted index each stock in
the index has the same number of shares and that number is equal to 1 divided by
the divisor of the index. In the last example above, with the divisor equal to 1.21943,
there would be 1/1.21943 or 0.82 shares of each stock in the index. Thus any stock
that was up by 1 point during a given day would be contributing an upward move
ment of 0.82 points in the index. Before the split there were 0.60 (1/1.65843) shares
of each stock
Another way to look at the revision of a price-weighted index following a split
by one of its stocks is the following: If one stock splits, then to reestablish the fact that
there are an equal number of shares of each stock in the index, part of the extra (split)
shares should be sold off and used to buy an equal number of shares of each of the
remaining stocks. Note that before the split there were 0.60 shares of each stock, and
0.82 shares after. When stock B split 2-for-I, it increased its shares from 0.60 to 1.20,
so to rebalance the index it was necessary to sell 0.38 shares of stock Band use the
proceeds to buy 0.22 shares of each of stocks A and C.
A price-weighted index's divisor can be subject to fairly frequent revision, just
as was the case with the capitalization-weighted index. These divisors are maintained
by the organizations responsible for originating them, and they can be easily obtained
just by calling the proper organization. The most popular price-weighted indices are
the various DowJones indices and the Major Market Index (XMI).
The stock with the most weight in a price-weighted index is the one with the
highest price, which is substantially different from the capitalization-weighted index
where the stock with the most weight is the one with the most market value. Thus,
in the above examples, the stock with the greatest weight in the index would be stock
B before the split and C after the split. Of course, the matter of a stock's volatility has
something to do with which stock has the most weight in the change of the value of
the index. Thus, if stock B was the highest-priced stock at $90 per share, but had a
very low volatility, then its price changes would be small and it might consequently
not have as great an influence on the changes in the price of the index as some lower
priced stock would.
In general, one is far less concerned with a stock's weight in a price-weighted
index than


n the change of the value of
the index. Thus, if stock B was the highest-priced stock at $90 per share, but had a
very low volatility, then its price changes would be small and it might consequently
not have as great an influence on the changes in the price of the index as some lower
priced stock would.
In general, one is far less concerned with a stock's weight in a price-weighted
index than he is in a capitalization-weighted index. That is, one might notice that four
or five large stocks - IBM, AT&T, Exxon, General Motors, and General Electric, for
example - might make up over 30% of the S&P 100 even though they represent only
5% of the stocks in the index. However, the same five stocks in a price-weighted
index of 100 stocks would probably account for very nearly 5% of the index because
their prices are not substantially different from those of the other 95 stocks ( even
though their capitalizations are). So if one were to notice a large change in the price
500 Part V: Index Options and Futures
of IBM, one might figure that capitalization-weighted indices that contained that
stock would also be showing somewhat unusual price changes in the same direction
that IBM is moving. A price-weighted index that contained IBM would, of course,
also be affected by IBM's price change, but not extraordinarily so since IBM would
have far less weight in the price-weighted index.
SECTORS
Sector is a term used to refer to an index of stocks in which all the stocks are mem
bers of the same industry group. Examples of groups on which sectors have been cre
ated - and on which options have traded - are computers and technology, interna
tional oils, domestic oils, gold, transportation, airlines, and gaming and hotels. These
indices are computed in the same ways as described above - either price-weighted
or capitalization-weighted. They generally consist of fewer stocks than their major
counterparts, however. Most sectors are comprised of between 20 and 30 stocks,
since that is about all of the stocks in any one specific industry group. The large
indices are usually referred to as "broad-based" indices, as opposed to the smaller
sectors which are often referred to as "narrow-based" indices.
Options trade on these sectors. The intent of these options is to allow portfolio
managers -who often are group-oriented- to be able to hedge off parts of their port
folio by industry group. The options on these sectors are usually cash-based options.
Strategies will be discussed later, but there is not much difference in strategy
between broad-based or narrow-based index options. One difference is that broad
based option writers receive more favorable margin treatment ( that is, they are
required to put up less collateral) than narrow-based option writers.
CASH-BASED OPTIONS
Now that the reader is familiar with indices, let us look at the most popular type of
listed index option, the cash-based option.
Cash-based options do not have any physical entity underlying the option con
tract. Rather, if the option is exercised or assigned, the settlement is done with cash
only - there is no equity involved. This type of option is generally issued on an index,
such as the S&P 500, for which it would be virtually impossible to actually deliver the
underlying securities in case of assignment or exercise.
Since many investors feel that it is easier to predict the market's movement
rather than that of an individual stock, the cash-based index option has become very
popular. Other indices that underlie cash-based option contracts are the New York
Stock Exchange Index, the S&P 500 Index, the S&P 100 Index (OEX - an index
Chapter 29: lntrodudion to Index Option Produds and Futures S01
introduced by the CBOE), the NASDAQ Index ($NDX), the Dow-Jones 30
Industrials ($DIX), and several other indices. In each of these cases there are too
many stocks in the index, and too many varying quantities of each of the stocks, to be
able to handle the physical delivery of each of the stocks in the case of exercise or
assignment. Some cash-based options are based on subindices ( that is, subgroups of
the larger indices such as the transportation group).
EXERCISE AND ASSIGNMENT
It is important to understand the ramifications of exercise and assignment when deal
ing with this type of option. When a cash-based option is exercised, the owner
receives cash equal to the difference between the index's closing price and the strike
price of the option. The option writer who is assigned must pay out an equal amount.
The following example shows how a call exercise might work. In this and the follow
ing examples we will use a fictional index '.lYX (index symbols often end in X).
Example: Suppose an investor buys a '.lYX September 160 call option. At a later date,
the index has risen substantially in price and closes at 175.24 on a particular day. The
investor decides it is time to take his profit by exercising his call option. Assuming the
'.lYX contract is worth $100 per point, just as stock options are, he receives cash in
the amount of $100 times the difference between the index closing price and the
strike price: $100 x (175.24 - 160.00) = $1,524. He has no further position or rights
- the option position disappears from his account by virtue of the exercise and he
does not acquire any security by the exercise; he gets only cash.
An assignment would work in a similar manner, with the seller of an option hav
ing to pay out of his account cash equal to the difference between the index closing
price and the option's striking price. As an example, suppose that a trader sells a put
option on the '.lYX Index - the October 165 put. Subsequently, the index drops in
price, and one morning the writer of this put option finds that he has been assigned
(as of the previous day, as is the case with stock options). If the index closed at 157.58
on the previous day, then the option writer's account will be deb


ption's striking price. As an example, suppose that a trader sells a put
option on the '.lYX Index - the October 165 put. Subsequently, the index drops in
price, and one morning the writer of this put option finds that he has been assigned
(as of the previous day, as is the case with stock options). If the index closed at 157.58
on the previous day, then the option writer's account will be debited an amount equal
to $100 X (165.00 - 157.58) = $742.
EUROPEAN VERSUS AMERICAN EXERCISE
Before proceeding with more examples of index option exercise and the accompany
ing strategies, it is necessary to introduce two new definitions. American exercise
means that an option may he exercised at any time; European exercise means that an
option may only be exercised on its expiration day. Many of the cash-based index
502 Part V: Index Options and Futures
options have the European exercise feature. All stock options and some index options
have the American exercise feature.
The European exercise feature was introduced because institutional investors
who might tend to write calls against their portfolio of stocks wanted some assurance
that their protection wouldn't be unexpectedly taken away from them. Thus several
index option series became European exercise. Two major ones are the cash-based
index options on the S&P 500 Index (SPX) and the cash-based options on the Dow
Jones 30 Industrials. OEX remains an American exercise.
In-the-money European put options will be cheaper than their American coun
terparts. This is because an arbitrageur would have to carry the position all the way
to expiration; he could not exercise his puts and liquidate the position immediately.
In fact, deeply in-the-money European puts will trade at a discount; the higher short
term interest rates are, the deeper the discount will be.
This can affect the full protective capability of long-term European puts. If a
portfolio manager buys puts to protect his portfolio and the market crashes, the puts
might be deeply in the money. If these puts have a European exercise feature, they
would be selling at a deep discount and therefore would not have afforded all the
price protection that the portfolio manager had been looking for.
American Exercise Consideration. The primary reason for the holder of an
index option to exercise the option is to take his profit. One might think that, if the
holder wanted to take a profit, he would merely sell his option in the open market.
Of course, if he could, he would. However, many times the deeply in-the-money
options sell at a substantial discount during the trading day. A deep discount is con
sidered to be 1/2 to 3/4 of a point, or more. Near the end of the day, these options
tend to trade at only slight discounts. In either case, the holder of the option may
decide to exercise rather than to sell at any discount. Of course, if one is the holder
of a call option that is trading at a substantial discount in the morning of a particular
day, and he decides to exercise, he may lose more by the end of the day (if the mar
ket trades down) than he would have if he had merely sold at the deep discount in
the first place. In fact, some theoreticians feel that the "job" of a deeply in-the-money
cash-based option during the trading day is to try to predict the market's close. This,
of course, is not a "job" that can be consistently done with accuracy (if it could, the
traders doing the predicting would be rich beyond their wildest dreams).
If the holder of a cash-based call option turned bearish, that would be another
reason to exercise. That's right - if the holder of a cash-based call option is bearish,
he should exercise because, by so doing, he liquidates his bullish position and takes
his profit. This is somewhat opposite from an option that has a physical underlying
security, such as a stock option. This presents an interesting scenario: If one turns
Chapter 29: Introduction to Index Option Products and Futures 503
bearish late in the day, even after the close, he might conceivably try to exercise his
calls to liquidate his position. The exchanges recognize that such tactics might not be
in everyone's best interest - for example, if one waited to see how the money supply
numbers looked on a particular evening before exercising, he would definitely have
an advantage over the writers of those same options. The writers could no longer
viably hedge their positions after the market had closed. In order to prevent this,
cash-based option exercise notices are only acceptable until 5 minutes after the
options close trading on that exchange on any given trading day ( except expiration, of
course), in order to allow both holders and writers to be on somewhat equal footing.
There is one more fact regarding exercise of cash-based options that will inter
est brokerage customers, retail or institutional. Most brokerage firms will charge a
commission for the cash-based option exercise or assignment. When index options
were first traded, commissions were quite high. Currently, however, one should gen
erally be paying a commission based upon the equivalent option price.
Example: In the previous example, one exercised a ZYX Sep 160 call at expiration
when the index closed at 175.24. This is a differential of 15.24. One should pay a
commission as if he had sold his long calls at a price of 15.24, not on anything more.
For writers of cash-based options, things are not so different from stock options.
The writer is still warned of impending assignment by the fact that the option is trad
ing at a discount. If it is not trading at a discount, it is probably not in danger of being
assigned. Also, since there is no stock involved and therefore no dividends paid, the
writer of a cash-based put option need only be concerned with whether the put is
trading at a discount, not with whether it is trading at a discount to underlying price
less the dividend, as is the c


he option is trad
ing at a discount. If it is not trading at a discount, it is probably not in danger of being
assigned. Also, since there is no stock involved and therefore no dividends paid, the
writer of a cash-based put option need only be concerned with whether the put is
trading at a discount, not with whether it is trading at a discount to underlying price
less the dividend, as is the case with stock options.
Traders doing spreads in cash-based options have special worries, however.
What may seem to be a limited-risk spread may acquire more risk than one initially
perceived, due to early assignment of the short options in the spread. Consider the
following example.
Example: Suppose that an investor establishes a bearish call spread in ZYX options
- he buys the November 160 call at a price of 1 and simultaneously sells the
November 155 call at 3. His risk on the spread is $300 plus commissions if he has to
pay the maximum, limited debit of $500 to buy back the spread, or so it appears.
However, suppose that the index rises substantially in price and the spreader is
assigned on the short side of his spread with the index at 175.24. He thus is charged
a debit of $2,024 to "cover" each short call via the assignment: $100 times the in-the
money amount, 175.24 - 155.00, or 20.24. He receives this assignment notice in the
504 Part V: Index Options and Futures
morning before the next trading day begins. Note that he cannot merely exercise his
long, since, if he did that, he would then receive the next night's closing price for his
long. Under the worst scenario, suppose the market receives disappointing econom
ic news the next day and opens sharply lower - with the index at 172. If he sells his
long Nov 160 calls at parity ($1,200), he will have paid a debit of $824 - larger than
his initial, theoretically "limited" maximum debit of $500. Thus he loses $624 on this
spread ( $824 less the initial credit of $200) - over twice the theoretically limited loss
of $300.
If the market should open sharply lower and trade down, he could lose more
money than he thought because his long position is now exposed - there is no longer
a spread in place after the short option is assigned. Of course, this could work to his
advantage if the market rallied the next day. The point is, however, that a spread in
cash-based options acquires more risk than the difference in the strikes (the maxi
mum risk in stock options) if the short option in the spread becomes a deeply in-the
money option, ripe for assignment.
NAKED MARGIN
When an index is designated as "broad-based," a lesser margin requirement applies
to the writer of naked options. The SEC determines which indices are broad-based.
A broad-based index receives more favorable margin treatment because the under
lying index will not normally change in price as quickly as a stock or subindex. Thus,
the naked writer theoretically has less of a risk with a naked broad-based index
option.
The requirement for writing a broad-based index option naked is 15% of the
index, plus the option premium, minus the amount, if any, that the option is out-of
the-money. There is a minimum requirement: for calls, it is 10% of the index value;
for puts, it is 10% of the striking price. Both minima are in addition to the option pre
mium.
Example: Suppose that the ZYX is at 168.00, with a Dec 170 call selling for 6 and a
Dec 170 put selling for 5. The requirement for selling the call naked would be cal
culated as follows:
15% of index
Plus call premium
Less out-of-money amount
Naked call requirement
$2,520
+ 600
200
$2,920
Chapter 29: Introduction to Index Option Produds and Futures
The requirement for writing the Dec 170 put naked would be:
15% of index
Plus put premium
Naked put requirement
$2,520
+ 500
$3,020
Both of these requirements are above the minimum of 10% of the index.
505
Options on narrow-based indices are subject to the same naked requirements
as stock options: 20% of the index plus the premium less an out-of-the-money
amount, with a minimum requirement of 15% of the index.
Other margin requirements are similar to those for stock options. For example,
if one wanted to write the Dec 170 straddle naked, using the same prices as in the
last example, he would have a margin requirement equal to $3,020 - the larger of the
put or call requirement, just as he would for stock options. Spread requirements for
index options work in exactly the same manner as they do for stock options.
LEAPS INDEX OPTIONS
LEAPS (Long-term Equity AnticiPation Securities) have been introduced on indices
in recent years. Readers not familiar with LEAPS should review the prior chapter on
that subject. Since LEAPS have become popular for stocks, it is only logical to think
that they would become popular for indices as well.
The main problem was that a LEAPS could be a 2-year option on a 350 dollar
underlying index. Such an option might cost 20 points. That is too expensive to attract
the public customer. Just one option would cost $2,000. Therefore, the exchanges
created mini-indices out of OEX, SPX, XMI, and others. These mini-indices that
were created are exactly the same as the full indices, except that they are divided by
10. This means that instead of having the 2-year put with strike of 350 cost 20 points,
a 2-year put with a strike of 35 costs 2 points. This is much more affordable for the
individual trader.
The following example is of OEX options and the corresponding OAX LEAPS
options on the same index. NOTE: OAX is not the universal symbol for this mini
index. OEX LEAPS are American exercise, while SPX LEAPS are European. A bro
ker should be contacted for symbols, expiration dates, and other details.
Example: The following is a sample comparison of prices for OEX and for its com
panion index OLX, which is OEX divided by 5. (Originally, OLX was OEX divided by
10, but when OEX split 2-for-1 in late 1997, OLX did


he universal symbol for this mini
index. OEX LEAPS are American exercise, while SPX LEAPS are European. A bro
ker should be contacted for symbols, expiration dates, and other details.
Example: The following is a sample comparison of prices for OEX and for its com
panion index OLX, which is OEX divided by 5. (Originally, OLX was OEX divided by
10, but when OEX split 2-for-1 in late 1997, OLX did not split so OLX was thereafter
equal to OEX divided by 5).
506
OEX: 712
Part V: Index Options and Futures
OLX: 142.40
OLX 2-year LEAPS options:
Dec 140 call: 30
Dec 150 call: 26.5
Dec 160 call: 20.5
Note that striking prices of 140, 150, and 160 for OLX correspond to 700, 750, and
800 for OEX itself. Also, if a 2-year OEX Dec 700 call existed, it would sell for
approximately five times as much as the OLX Dec 140 call, or about 150 points (5
times 30). This is why the LEAPS options use reduced-value strikes, because very
few people would have interest in trading an at-the-money option that cost 150
points ($15,000).
FUTURES
We will now take a look at how futures contracts work. This section will be concerned
only with cash-based index futures; futures for physical delivery are included in a
later chapter. The ordinary stock investor might think that he will be able to employ
index option strategies without getting involved in futures. While it may be possible
to avoid futures, the strategist will realize that they are a necessary part of the entire
index-trading strategy. Thus, in order to be completely prepared to hedge one's posi
tions and to operate in an optimum manner, the use of index futures or index futures
options is a necessary complement to nearly all index strategies.
A comnwdities futures contract is a standardized contract calling for the deliv
ery of a specified quantity of a certain comnwdity at some future time. The older,
more conventional types of commodities contracts were futures on grains, meats, and
metals. In recent years, futures have expanded extensively and have encompassed
financial securities - bonds, T-bills, Eurodollar Time Deposits, etc. Most recently,
futures have been issued that are cash-based; that is, no actual commodity is deliver
able. Rather, the contract settles for cash. Some of these cash-based futures contracts
have stock market indices as their underlying 'commodity. "It is this latter type of
future that will be the subject of the examples in this section, although the basic facts
regarding futures are applicable to all futures contracts, cash-based or not.
Several types of traders or investors use futures contracts. One is the specula
tor: He is able to generate tremendous leverage with futures and may be able to cap
italize on small swings in the price of the underlying commodity. Another is the true
hedger: He is a dealer in the actual underlying commodity and uses futures to hedge
his price risk. This is the more economic function of futures. Examples of hedges for
physical commodities as well as stocks will be presented in later chapters. However,
Chapter 29: Introduction to Index Option Products and Futures 507
let us look at a simple example of how one might hedge a stock portfolio with stock
index futures.
Example: Suppose that a stock mutual fund operates under the philosophy that
investors cannot outperform a bullish market, so the best investment strategy when
one is bullish is just to "buy the market." That is, this mutual fund actually buys all
the stocks in the Standard & Poor's 500 Index and holds them.
If the manager of this fund turns bearish, he would want to sell out his positions.
However, the commission costs for liquidating the entire portfolio would be large.
Also, the act of selling so much stock might actually depress the market, thereby
devaluing the remainder of his portfolio before he can sell it.
This manager might sell S&P 500 futures against his portfolio instead of selling
his stocks. Such a futures contract would move up or down in line with the S&P 500
Index as it rises or falls. Suppose that he sold enough futures to hedge the entire dol
lar value of his stock portfolio. Then, even if the stock market declined, his futures
contracts would decline also and would theoretically prevent him from having a loss.
Of course, he couldn't make much of a gain if the market went up, since the futures
would then lose money. What this money manager has accomplished is that he has
effectively sold his stock portfolio without incurring stock commission costs (futures
commissions are normally quite small).
If he turns bullish again at some later date, he can buy the futures back, and
have his long stocks free to profit if the market rises. Again, he does not spend the
stock commission nor does he have to go through the tedious process of placing 500
stock orders to "buy" the S&P 500 - he merely places one order in futures contracts.
Futures contracts often trade at premiums to the underlying commodity, due to
the fact that the investor who buys the future does not have to spend the money that
one who buys all the stocks would have to spend. Thus, he saves the carrying costs
but forsakes any dividends. This savings is reflected by the marketplace in that a pre
mium is placed on the price of the futures contract. As a consequence, longer-term
contracts trade at a larger premium than do near-term contracts, much as is the case
with options. In most cases, however, the index futures trader is concerned with the
nearest-term contract, and perhaps the next one out in time.
TERMS OF THE CONTRACT
There are cash-based index futures on several indices, although some of these futures
contracts are not heavily traded. The most heavily traded contract is the future on the
S&P 500 Index. This contract trades on the Chicago Mercantile Exchange. It has con
tracts that expire every 3 months (March, June, September, December) and a 1-point
508 Part V: Index Options and Futures
mov


THE CONTRACT
There are cash-based index futures on several indices, although some of these futures
contracts are not heavily traded. The most heavily traded contract is the future on the
S&P 500 Index. This contract trades on the Chicago Mercantile Exchange. It has con
tracts that expire every 3 months (March, June, September, December) and a 1-point
508 Part V: Index Options and Futures
move in the futures contract is worth $250. There is no particular reason why a I-point
move is worth $250, that is merely how the contract is defined. These numbers are
subject to change. Originally, a I-point move in S&P futures was worth $500, but
when the S&P advanced so much during the bull market of the 1990's, the point value
was halved in order to reduce the trading exposure in trader's accounts. One could
surmise that a further bull market advance might cause the number to be reduced
again, or possibly a prolonged bear market could result in an increase from $250 back
to $500, conceivably.
Example: A futures trader buys I March S&P 500 contract at 401.00 (the smallest
unit of trading is 0.10 points, a "dime"). The contract rises in price to 403.30. The
trader has a profit of 2.30 points, or $575 (2.30 points x $250 per point).
The terms of futures contracts can change as the exchanges on which they are
traded attempt to adjust the contracts to he more competitive in the current trading
environment. Consequently, the strategist should check with his broker to determine
the exact terms of any contract before he begins trading it.
OPEN OUTCRY
Futures contracts trade on listed commodity exchanges. However, the method of
trading is different from that used for stocks and options. Futures trade by "open
outcry" in rings or pits. Members of the exchange are the only ones allowed to trade
on the exchange, of course, just as is the case with stocks and options. If the. member
is trying to execute a buy order, for example, he would announce his bid out loud
(open outcry). Sellers would then respond by either showing him an offer or by sell
ing to him at his bid price. This differs from stocks and options which use the spe
cialist system, in that many people can be buying and selling at once, all over the pit.
It also differs from the market-maker system used on some stock options exchanges
because anyone can make the market in the commodity pit, not just a designated few
traders.
This form of trading can produce some oddities not normally associated with
stock or stock option trading. There may be slightly different markets at different
places in a large, busy trading pit. Hence a buyer on one side of the pit may be try
ing to pay a price that is being offered on the other side of the pit, but the two do not
trade with each other because of the size of the trading crowd. The buyer might buy
on one side of the pit, but the seller on the other side does not sell. Then if the mar
ket trades lower, only one of the two will have received an execution even though
they were trying to buy and sell at the same price. Thus, one cannot be certain that
his futures order is executed unless the market trades through his price. That is, if
Chapter 29: Introduction to Index Option Products and Futures 509
one is bidding for futures at a price of 1401.50 and a trade is printed at 1401.40, then
he can be certain that he has bought his contracts.
Futures exchange members who trade mainly for their own account from the
ring or pit are known as locals." They are somewhat akin to the stock option market
maker in that they may take the other side of public orders. Note, however, that they
do not have to make a public market as market-makers do.
MARGIN, LIMITS, AND QUOTES
Futures contracts are traded on margin and are marked to market every day.
Generally, the amount of margin required is small in comparison to the total size of
the contract, so that there is tremendous leverage in trading futures. Anyone trading
the futures must deposit the initial margin amount in his account on the day he ini
tiates the trade. Then at the end of each day, the amount of gain or loss on the con
tract is computed, and the account is credited if there is a gain or debited if there is
a loss. In case of a loss, the trader must add more cash to his account to cover the
loss. This daily margin computation is known as maintenance margin. Treasury bills
or other securities are good collateral for the initial margin, but the daily variation
margin is required in cash.
Example: The S&P 500 futures contract is a cash-based futures contract that trades
on the Chicago Mercantile Exchange. Since the contract is settled in cash, there is
no actual physical commodity underlying the contract. Rather, the contract is based
on the value of the S&P 500 stock index. At the expiration of the contract, each open
contract is marked to market at the closing price of the S&P 500 stock index and dis
appears. All contracts are settled for cash on their final day and then they no longer
exist - they expire. The terms of the contract specify that each point of movement is
worth $250. Thus, if the S&P 500 Index itself is at 1405, then the S&P futures con
tract is a contract on $250 x 1405, or $351,250 worth of stocks comprising the index.
Assume the initial margin for one of these contracts is $30,000, although it may vary
at specific brokerage houses.
Suppose that a trader buys one December S&P futures contract for his account
sometime in October. With the underlying index at 1405.00, suppose he pays 1417.50
for the futures contract. It is normal for the futures to trade at a premium to the actu
al index price. The reasons regarding this will be discussed in a later section. Initially,
the customer puts up $30,000 as margin, and this may be in the form of T-bills. On
the next day, however, the market declines and the futures close at 1406.00. This rep
resents a loss of 11.50 points from the purchase price. A


utures contract. It is normal for the futures to trade at a premium to the actu
al index price. The reasons regarding this will be discussed in a later section. Initially,
the customer puts up $30,000 as margin, and this may be in the form of T-bills. On
the next day, however, the market declines and the futures close at 1406.00. This rep
resents a loss of 11.50 points from the purchase price. At $250 per point, the trader
has a loss of $2,875 (250 x 11.50) at this time. He is required to add $2,875 in cash
into the account.
510 Part V: Index Options and Futures
If he continued to hold the contract until expiration, this process of adding his
daily gain or subtracting his daily loss from the account would recur each day. Finally,
on the last day, the futures contract is deemed to close at the exact opening price of
the S&P 500 Index and the variation margin is calculated again at that price. Then
the futures contract is expired, so it is "erased" from his account. He is then left with
only the cash that he made or lost on the trade of his contract.
The leverage produced by small margin requirements (as a percent of the total
value of the contract) is a major factor in making futures very volatile, in dollar terms.
In the preceding example, a $30,000 margin investment controls $351,250 worth of
stocks. Due to their volatility, many futures contracts trade with a limit. That is, the
price can only fluctuate a fixed amount above or below the previous day's closing
price. This concept is intended to prevent traders with large positions from being
able to manipulate the market drastically in either direction.
S&P and NYSE Expiration. S&P 500 futures expiration occurs in a some
what complex way, compared to those indices whose options and futures expire
at the last sale on the final day of trading. Some years ago, in order to attempt
to reduce the volatility that index futures and options expiration was causing in
the stock market, the NYSE and the Chicago Mercantile Exchange (where the
S&P 500 futures trade) agreed to change the expiration of their index products
from the end of trading on the last Friday to the morning of that day. The effect
of expiration on the stock market is discussed in the next chapter.
As a result, the S&P futures and futures options as well as futures, futures
options, and index options on the New York Stock Exchange Index settle in the fol
lowing manner on their last day of trading. On expiration day - the third Friday of
the month - the "final" price for purposes of settling futures and options is comprised
of taking the opening trade of each stock and calculating an index price based on
those opening prices. There is no actual trading in the futures and options on that last
Friday; they cease trading at the close of trading on the previous day, Thursday.
The purpose of this change was to give the specialists on the New York Stock
Exchange more time to line up the other side of trades to handle order imbalances.
Under the new rules, index arbitrageurs are forced to enter their buy or sell orders
as market on open orders on that last Friday before 9 am EST. The specialist can then
take his time in opening the stock if he needs to; he can solicit orders if there is too
much stock to buy or sell.
The effect of all this is that the "final" index price for settlement purposes is not
known until all the stocks in the index have opened. It may take some time to open
all 500 stocks in the S&P 500 Index if there is a volatile market that Friday morning
Chapter 29: Introduction to Index Option Products and Futures 511
(perhaps caused by news) or if there are severe order imbalances in many of the
stocks (caused by index arbitrageurs). Index arbitrage is described in Chapter 30.
Limits. Originally, index futures traded without limits. However, the stock mar
ket crash of 1987 changed that. Certain parties felt that if the futures - which
were leading the market down - had ceased trading for a while, the stock mar
ket could have stabilized. As a result, a series of trading limits now exists for
stock index futures. These are designed to be "circuit breakers" - to prevent a
stock market crash. They are not limits in the sense that other futures have lim
its, but they are similar.
The levels at which these circuit breakers occur may change from time to time,
based on the volatility of the stock market and the price levels at which the S&P
futures are trading. That is, if the S&P futures are trading at 1500, one can expect
wider circuit breakers than if they are trading at 600. These circuit breakers only
apply to downside moves by the stock market. The first in the series of circuit break
ers usually halts trading for only 10 minutes. After that, if the market trades lower -
usually something on the order of a 10% decline - then a longer circuit breaker is
instituted for about 30 minutes or so. After that they could open again, and if they
reached the next limit down - something probably on the order of 20% then trad
ing would be halted for a longer time ( two hours or so again, the details depend on
the current regulations). If there is any time left in the trading day, they can open
again, and trade down to a final limit, at which time trading would be halted for the
day. They could not trade any lower that day, although they could trade lower the
next day if need be.
There are similar limits imposed by the NYSE on its trading - based on the
Dow-Jones Industrial Averages. Those limits don't necessarily line up exactly with the
limits on the S&P futures. That fact might cause problems for hedgers should any of
these severe downside limits actually occur.
There are actually other "circuit breakers" designed to prevent runaway stock
markets, but they are not related to limits on futures trading. They will be described
along with index arbitrage and program trading in Chapter 30.
Quotes. While stocks and stock option


limits on the S&P futures. That fact might cause problems for hedgers should any of
these severe downside limits actually occur.
There are actually other "circuit breakers" designed to prevent runaway stock
markets, but they are not related to limits on futures trading. They will be described
along with index arbitrage and program trading in Chapter 30.
Quotes. While stocks and stock options are always quoted in dimes, or some
times nickels, such is not the case with futures. Some futures trade in fractions,
while others trade in cents. In the coming chapters, there will be many examples
of the trading details of futures and options. However, the investor should famil
iarize himself with the details of an individual contract before beginning to trade
it or its options. One's commodity broker can easily supply this information.
512 Part V: Index Options and Futures
There are certain differences between the way futures trade and the way stocks
trade. One difference that is extremely important to investors accustomed to dealing
in stocks and stock options is that quotation vendors rarely show a bid and offer for
futures. Thus, if one uses a quote machine to obtain the price of a stock he might see
that the stock is currently 31 bid, 31.10 asked, with a last sale of 31. An active futures
contract traded on a trading floor (which is typically the type that one would want to
trade) virtually never shows a bid and offer, but rather shows last sale only. In addi
tion, each sale of a stock or stock option is recorded both as to its time of execution
and the quantity of execution. Such is not the case for futures. Only the price is
recorded - one cannot tell how many contracts traded at the price, nor can he tell if
there were repeated sales at that price. Where futures are traded in electronic mar
kets, of course, the bid and offer are available for all to see, and volume may accu
rately be recorded as well.
OPTIONS ON INDEX FUTURES
As we saw earlier, futures contracts allow a person dealing in a commodity to minimize
profit fluctuations in his commodity. The mutual fund manager who sold the futures
largely removed any possibility of further upside profit or downside loss. Options,
however, allow a little more leeway than futures do. With the option, a person can lock
in one side of his position, but can leave room for further profits if conditions improve.
For example, the mutual fund manager might buy put options on the S&P 500 Index
to hedge his downside risk, but still leave room for upside profits if the stock market
rises. This is different from the sale of a futures contract, which locks in his profit, but
does not leave any room for further profits if the market moves favorably.
Options trade on many types of futures contracts. The security underlying the
option is the futures contract having the same expiration month, not the entity under
lying the futures contract itself. Thus, if one exercises a listed futures option, he
receives a futures contract position, not the physical commodity.
Example: A trader owns the ZYX futures December 165 call option (165 is the strik
ing price). Assume the ZYX December future closed at 171.20. Both the calls and the
futures are worth $500 per point. If the call is exercised, the trader then owns one
ZYX December (same expiration month as the option) futures contract at a price of
165. Since the current price is 171.20, there is a maintenance margin credit of $3,100
in his account (500 x 6.20 points). Note that even though the option is an option on
a future which is cash-based, the exercise provides the holder of the option with a
futures contract position, not with cash.
Chapter 29: Introduction to Index Option Products and Futures 513
At the present time, there are futures options on all of the various index futures
contracts.
EXPIRATION DATES
Futures options have specifics much the same as stock options do: expiration month
(agreeing with the expiration months of the underlying futures contract), striking
price, etc. If a trader buys a futures option, he must pay for it in full, just as with stock
options. Margin requirements vary for naked futures options, but are generally more
lenient than stock options. Often, the naked requirement is based on the futures
margin, which is much less than the 20% of the underlying stock price as is the case
with listed stock options.
When the futures option has a cash-based futures contract underlying it, the
option and the future generally expire on the same day. Thus, if one were to exercise
a '.ZYX option on expiration day, one would receive the future in his account, which
would in tum become cash because the future is cash-settled and expiring as well.
Example: Suppose that a trader owns a '.ZYX December 165 futures worth $500 per
point - call option and holds it through the last day of trading. On that last day, the
'.ZYX Index closes at 174.00. He gives instructions to exercise the call, so the follow
ing sequence occurs:
1. Buy one '.ZYX future at 165.00 via the call exercise.
2. Mark the future at 17 4.00, the closing price. This is a variation margin profit of
$4,500 (174.00-165.00) X $500.
3. The option is removed from the account because it was exercised, and the future
is removed as well because it expired.
Thus, the exercise of the option generates $4,500 in cash into the account and leaves
behind no futures or option contracts. We do not know if this represents a profit or
loss for this call holder, since we do not know if his original cost was greater than
$4,500 or not.
It should be noted that futures option expiration dates, in general, are fairly
complex. They are not normally the third Friday of the expiration month, as stock
options are. Index futures options generally do expire on the third Friday of the expi
ration month, but many physical commodity options do not. These differences will
be discussed in the later chapter


as greater than
$4,500 or not.
It should be noted that futures option expiration dates, in general, are fairly
complex. They are not normally the third Friday of the expiration month, as stock
options are. Index futures options generally do expire on the third Friday of the expi
ration month, but many physical commodity options do not. These differences will
be discussed in the later chapter on futures options.
514 Part V: Index Options and Futures
OPTION PREMIUMS
The dollar amount of trading of a futures option contract is normally the same as that
of the underlying future. That is, since the S&P 500 future is worth $250 per point,
so are the S&P 500 futures options. The same holds true for the New York Stock
Exchange Index options.
Example: An investor buys an S&P 500 December 1410 call for 4.20 with the index
at 1409.50. The cost of the call is $1,050 (4.20 x 250). The call must be paid for in
full, as with equity options.
An interesting fact about futures options is that the longer-term options have a
"double premium" effect. The option itself has time value premium and its underly
ing security, the future, also has a premium over the physical commodity. This phe
nomenon can produce some rather startling prices when looking at calendar spreads.
Example: The ZYX Index is trading at 162.00 sometime during the month of
January. Suppose that the March ZYX futures contract is trading at 163.50 and the
June futures contract at 167.50. These prices are reasonable in that they represent a
premium over the index itself which is 162.00. These premiums are related to the
amount of time remaining until the expiration of the futures contract.
Now, however, let us look at two options - the March 165 put and the June 165
put. The March 165 put might be trading at 3 with its underlying security, the March
futures contract, trading at 163.50. The June 165 put option has as its underlying
security the June futures contract. Since the June option has more time remaining
until expiration, it will have more time value premium than a March option would.
However, the underlying June future is trading at 167.50, so the June 165 put option
is 2½ points out-of-the-money and therefore might be selling for 2½. This makes a
very strange-looking calendar spread with the longer-term option selling at 2½ and
the near-term option selling for 3. This is due to the fact, of course, that the two
options have different underlying securities. One is in-the-money and the other is
out-of-the-money. These two underlyings - the March and June futures - have a
price differential of their own. So the option calendar spread is inverted due to this
double premium effect.
FUTURES OPTION MARGIN
Most futures exchanges have gone to the form of option margin called SPAN, which
stands for Standard Portfolio Analysis of Risk. This form of margining is very fair and
attempts to base the margin requirement of an option position on the probability of
Chapter 29: Introduction to Index Option Products and Futures 515
movement by the underlying futures contract, as well as on the potential change of
implied volatility of the options in question.
The older method of margining option positions is known as the "customer mar~
gin" method. The customer margin method generally results in higher margin
requirements. The reader is referred to the chapter on futures and futures options
for an in-depth discussion of SPAN and other option margin requirements.
OTHER TERMS
Just as futures on differing physical commodities have differing terms, so do options
on those futures. Some options have striking prices 5 points apart while others have
strikes only 1 point apart, reflecting the volatility of the commodity. Specifically, for
index futures options, the S&P 500 options have striking prices 5 points apart, and
the NYSE options have striking prices 2 points apart.
There is no standard method for quoting futures on options as there is with
stock options. In some cases, striking price symbols are similar to stock option sym
bols (A=5, B=lO, C=l5, etc.), while in others the letters are used incrementally (A=l,
B=2, C=3, etc.). Moreover, the method used may differ with each quote vendor. In
some cases, quote systems use the numeric value of the strike instead of letters. This
makes quoting options much simpler, and perhaps the entire industry (including
stock option vendors) will adopt this method someday. Since there is no standard
method for quoting, one must obtain the symbols individually for futures options, a
fact that makes quoting them extremely inconvenient.
There are position limits for some futures options, hut they allow for very large
positions. Check with your broker for exact limits in the various futures options.
QUOTES
Most futures option quotes (bids and offers) are not displayed on quote-vending
machines, as is also the case with futures. Options traded on the Chicago Mercantile
Exchange are the exception. This can he somewhat distressing to the trader used to
dealing in stock options, since options are normally far less liquid than the underly
ing security. It might be acceptable to trade off of last sales in a liquid futures con
tract, but not so with the options. As a result, futures options have not attracted many
stock option traders into their fold. Of course, where electronic markets exist, the
bids and offers of options would be shown publicly.
The consequence of the inconsistencies in terms as well as the general unavail
ability of quotes has been that index futures options are generally traded by profes
sionals, with the public largely ignoring them. This does not mean, however, that
516 Part V: Index Options and Futures
futures options are unworthy of the strategist's time and effort. In fact, just the oppo
site may be true - the lack of general information may produce some inefficiencies
that the strategist can benefit from.
One factor concerning the tradi


ons are generally traded by profes
sionals, with the public largely ignoring them. This does not mean, however, that
516 Part V: Index Options and Futures
futures options are unworthy of the strategist's time and effort. In fact, just the oppo
site may be true - the lack of general information may produce some inefficiencies
that the strategist can benefit from.
One factor concerning the trading of futures options can be of major concern
to many customers and salesmen. Salesmen who are registered to sell stocks are not
necessarily registered to sell futures - an additional test must be passed in order to
sell many types of futures options. Similarly, many customers - primarily institutions
- have received approval from their constituents to trade in stock options, but would
need further approvals to trade futures or futures options. Neither of these things
should stand in the way of the strategist - if there are opportunities in futures
options, then the customer should find a broker who can trade them. Also if the
strategist finds that he requires certain approvals from within his own institution
before he can trade futures, then he should obtain those approvals.
STANDARD OPTIONS STRATEGIES USING INDEX OPTIONS
The stock option strategies described in all of the preceding chapters of this book can
be established with index options as well. The concepts are normally the same for
index options as they would be for stock options. If one buys a call at one strike and
sells a call at a higher strike, that is a bullish spread; if one sells both a put and a call
at the same strike (a straddle), that is a neutral strategy. One uses deltas to determine
how many options to sell against the ones that he buys in order to establish a delta
neutral strategy. Likewise, he uses the deltas to tell, along the way, how his position
is progressing and how to adjust it to keep it delta neutral.
We will not describe these same strategies over again. They have already been
described in detail. The risk of early assignment removing one side of a position can
alter some strategies. In some cases there are particular advantages or disadvantages
with index options and futures. Thus, we will briefly go over some major option
strategies, giving details pertaining to their usage as index option strategies.
OPTION BUYING
The most common reason for wanting to buy index options is to take advantage of the
diversification that they provide, in addition to the normal advantages that option
purchasing provides: leverage and limited dollar risk. Many people feel that it is eas
ier to predict the general market direction than it is to predict an individual stock's
direction. This feeling, can, of course, be put to good advantage by buying index
options. However, sometimes it is not better to buy the index options. In such cases,
it may actually be smarter to purchase a package of individual stock options.
Chapter 29: Introduction to Index Option Products and Futures 517
Due to a phenomenon known as volatility skewing, it is possible for index
options to have implied volatilities that are out of line with projected index or stock
price movements. This phenomenon is discussed in detail in the chapter on advanced
concepts.
For example, suppose that index puts are expensive, as they became after the
1987 stock market crash. When this happens it may actually be more profitable for a
trader who is bearish on the market to buy a package of equity puts instead of buy
ing index puts. The equity puts are forced to reflect the probability of stock price
movement because arbitrage strategies will keep them in line. They will therefore be
less expensive than index puts when this type of volatility skewing is present. Index
puts can remain expensive for several reasons - primarily excessive demand and
inflated margin requirements. In such situations, it is theoretically correct to buy a
group of puts on stock options. In fact, one might even hedge this purchase by sell
ing out-of-the money, overpriced index puts.
SELLING INDEX OPTIONS
In earlier chapters, we saw that many mathematically attractive strategies involve the
sale of naked options - ratio writes, straddles, ratio spreads, etc. Index options pres
ent an even stronger case for these strategies. Recall that the greatest risk in these
strategies with naked options is that the underlying security might move a great dis
tance, thereby exposing the position to great loss if the movement is in the direction
in which the naked options lie. That is, if one is naked calls and the underlying secu
rity rises dramatically, perhaps on a takeover bid, then large losses - potentially
unlimited in the absence of follow-up action - could occur.
The strategist would, of course, never let the loss run uncontrolled. He would
attempt to take some follow-up action to limit the loss or to neutralize the position.
However, even the best strategist cannot hedge his position if the movement in the
underlying occurs while the market is closed. For example, if the underlying securi
ty is a stock, certain news items might cause a large gap to occur between the closing
price of a stock and its next opening price. Such news might be related to a takeover
of the company or to a drastically negative earnings report, for example.
Index options do not have this particular drawback. An index - especially a
broad-based index - is not as likely to open on a wide gap as a stock is. An index can
not be the subject of a takeover attempt. It cannot be severely depressed by bad earn
ings on one of its components. Thus, index options are more viable candidates for
strategies involving naked option writing than stock options are. Index futures and
options may often open on small gaps of a point or so, due to emotion or possibly due
to the fact that a market that opens earlier (T-Bond futures, for example) has already
518 Part V: Index Options and Futures
made


d by bad earn
ings on one of its components. Thus, index options are more viable candidates for
strategies involving naked option writing than stock options are. Index futures and
options may often open on small gaps of a point or so, due to emotion or possibly due
to the fact that a market that opens earlier (T-Bond futures, for example) has already
518 Part V: Index Options and Futures
made a rather large move by the time the futures open. Such a small gap is normal
ly not extremely damaging to the naked writer.
One cannot assume that an index can never gap open widely - if something
drastic were to happen in the marketplace that caused opening gaps in many stocks,
then a gap could appear in the index itself. The worst case of such a gap, percentage
wise, was the stock market crash in 1987 when the major indices such as OEX and
S&P 500 opened down over 20 points. Nothing has come close to that before or
since, but the possibility always exists that it could happen again. Therefore, one can
not assume that naked option writing of index options is a low-risk strategy; howev
er, it is generally less risky than naked option writing of equity options.
HANDLING EARLY ASSIGNMENT OF CASH-BASED OPTIONS
The greatest problem that a spreader of index options has is the possibility of early
assignment. This removes his hedge on one side of his position, exposing him to
much more risk than he had wanted or anticipated.
One can often obtain a clue before early assignment occurs by observing the
price of the in-the-money options. If they are trading at a discount, one can expect
assignment to be more likely.
Example: '.lYX is trading at 357 a few days before expiration of the January options.
The stock market rallies heavily near the close, and the January 340 calls are trading
with a market of 16½ to 16¾ after 4 pm EST. Since parity is 17 for these calls, it is
likely that a writer will receive an assignment notice in the morning.
The strategist who observes this situation taking place must make a rather quick
decision. Since the market has rallied heavily on the close, it is likely that arbitrageurs
or institutional accounts who are long index options are going to exercise them. The
cynic among us would even think that they might be short stocks as well which they
plan to cover in the morning. Notice that the effect of hedged call option sellers (i.e.,
spreaders) receiving assignment notices will be to make them all long the market.
The short side of their spread will have been removed via assignment, and they will
be left with only the long side. Therefore, in order to liquidate or hedge, they will
have to sell stocks or index futures and options in the morning. This would force the
market down temporarily and would be a boon to anyone who was short overnight.
The spreader's first potential choice of action is to notice what is happening near
the close of trading and to try to exercise his long calls since he expects assignment
of his short calls. The assignment, of course, is not certain - he is merely projecting
it. Therefore, he could outfox himself and end up being very short if he did not
r~ceive an assignment notice on his short calls.
Chapter 29: Introduction to Index Option Products and Futures 519
Assuming the strategist did not anticipate assignment and therefore did not
exercise his long calls, he has several choices after receiving an assignment notice the
next morning. First, he could do nothing. This would be an overly aggressive bullish
stance for someone who was previously in a hedged position, but it is sometimes
done. The strategist who takes this aggressive tack is banking on the fact that the sell
ing after the assignment will be temporary, and the market will rebound thereafter,
giving him the opportunity to close out his remaining longs at favorable prices. This
is an overly aggressive strategy and is not recommended.
The most prudent approach to take when one receives an early assignment on
a cash-based option is to immediately try to do something to hedge the remaining
position. The simplest thing to do is to buy or sell futures, depending on whether the
assignment was on a put or call. If one was assigned on a put, a portion of the bull
ishness (short puts are bullish) of one's position has been removed. Therefore, one
might buy futures to quickly add some bullishness to the remaining position.
Generally, if one were assigned early on calls, part of the bearishness of his position
would have been removed - short calls being bearish - and he might therefore sell
futures to add bearishness to his remaining position. Once hedged, the position can
be removed during that trading day, if desired; by trading out of the hedge estab
lished that morning.
One should receive this assignment notice early in the morning, so he can
immediately hedge his position in the overnight markets. If he waits until the day ses
sion opens, he might use futures or options to hedge. One should be particularly
careful about placing market orders in an opening option rotation, especially on index
options after a severe downside move has occurred the previous day. Market makers
are very nervous and are not willing to sell puts as protection to the public in that sit
uation. Consequently, puts are notoriously overpriced after a large down day in the
stock market. One should refrain from buying put options in the opening rotation in
such a case. In the future, it is possible that comparable situations may exist on the
upside. To date, however, all gaps and severe mispricing anomalies have been on the
bearish side of the market, the downside.
CONCLUSION
The introduction of index products has opened some new areas for option strategists.
The ideas presented in this chapter form a foundation for exploring this new realm
of option strategies. Many traders are reluctant to trade futures options because
futures seem too foreign. Such should not b


nd severe mispricing anomalies have been on the
bearish side of the market, the downside.
CONCLUSION
The introduction of index products has opened some new areas for option strategists.
The ideas presented in this chapter form a foundation for exploring this new realm
of option strategies. Many traders are reluctant to trade futures options because
futures seem too foreign. Such should not be the case. By trading in futures options,
one can avail himself of the same strategies available in stock option. Moreover, he
may be able to take advantage of certain features of futures and futures options that
520 Part V: Index Options and Futures
are not available with stock options. For example, if one were to try to use options to
construct a strategy based on his expectation of interest rate movements, he could
use T-Bond futures and options, which is the easiest way. However, if he were to try
to remain with stock options, he would probably be forced to do something with util
ity stocks or illiquid interest rate options - a clearly inferior alternative.
Trading in index options can be very profitable, but only if one understands the
risks involved - especially the risk of early assignment in cash-based options. The
advantages to being able to "trade the market" as opposed to trading one stock at a
time are obvious: If one is right on the market, his index option strategies will be
profitable. This is superior to stock-oriented buying whereby one might be right on
the market, but not make any money because calls were bought on stocks that didn't
follow the market.
The strategist should consider all of his alternatives when trading in these mar
kets. If he is bullish, should he really be buying OEX calls? Maybe futures calls on
the S&P 500 are better. Perhaps the OEX is expensive with respect to the NYSE and
the NYA calls would be a better buy. In fact, perhaps all the calls are so expensive
that stock options are the best buy. The ideas presented in this chapter lay the
groundwork for the strategist to explore these questions and make the best decision
for his investment strategy.
Finally, keep in mind that the index futures and options comprise a very diverse
set of securities. They can be put to work for the investor, the trader, and the strate
gist in a multitude of ways. The only practical limit is in the mind of the user of these
derivative securities.
PUT-CALL RATIO
Generally, we have not been concerned with technical trading systems in this book.
Not that they aren't important, they are just in another category of investments other
than option strategies. However, the put-call ratio system is so closely related to
options that its inclusion is worthwhile.
The put-call ratio is simply the number of puts traded divided by the number
of calls traded. It can be computed daily, weekly, or over any other time period. It
can be computed for stock options, index options, or futures options. Sometimes it
is computed using open interest instead of volume. Another way to compute the put
call ratio is to divide the dollars spent on puts (sum of each put price times its trad
ing volume) divided by the dollars spent on calls (sum of each call price times its
trading volume). If it is calculated daily, one usually averages several days' worth of
figures to smooth out the fluctuations.
Chapter 29: Introduction to Index Option Products and Futures 521
Example: The morning paper shows that yesterday the trading activity for OEX
options was:
Total OEX Call Volume: 125,000 Contracts
Total OEX Put Volume: 135,000 Contracts
Therefore, the ratio is:
. 135 000 Index Put-Call Ratio= ' = 1.08 for yesterday
125,000
This technical indicator is a contrary one. The contrarian thinking is along these lines:
if everyone is buying puts, then everyone must be bearish; if everyone is doing some
thing, they can't all be right; therefore the contrarian must assume a bullish stance.
So, if the put-call ratio is high, too many traders are buying puts; a contrarian
would interpret that as a bullish sign. Conversely, if the put-call ratio is low, too many
traders are buying calls; the contrarian would consider that as a bearish indicator. The
theory behind contrary systems is that the majority of traders are wrong at major
turning points in the market.
There are several typical put-call ratios that can be computed. Generally, one
would not want to mix different types of options. For example, the equity put-call
ratio uses the option trading volume of equity options only. The index put-call ratio
uses index options only. Each futures contract put-call ratio is generally computed
separately, gold, soybeans, currencies, etc. One might also attempt to screen his input
a little further: for example, the index put-call ratio should only include index options
on U.S. exchanges; the others can be computed separately.
Obviously, the more highly traded option contracts produce a more reliable put
call ratio: equity options and index options being very liquid. Gold futures options by
themselves are not that active and may produce distorted results for a period of time.
The Ratio Itself. Traders and investors almost always buy more calls than
puts where stock options are concerned. Therefore, the equity put-call ratio is
normally a number far less than 1.00. If call buying is rampant, the equity put
call ratio may dip into the 0.30 range on a daily basis. Very bearish days may
occasionally produce numbers of 1.00 or higher. An average day will generally
produce a ratio of around 0.50.
Index options, however, produce much larger ratios. Many institutional and
other investors are constantly looking to avail themselves of the protective capability
of index puts. Therefore, far more index puts are purchased than are equity puts. An
average day might produce readings of 2.00 for some indices.
S22 Part V: Index Options and Futures
Interpreting the Ratio. There are sever


d 0.50.
Index options, however, produce much larger ratios. Many institutional and
other investors are constantly looking to avail themselves of the protective capability
of index puts. Therefore, far more index puts are purchased than are equity puts. An
average day might produce readings of 2.00 for some indices.
S22 Part V: Index Options and Futures
Interpreting the Ratio. There are several philosophies as to how to inter
pret the ratio once it has been calculated. All philosophies are of the contrarian
variety, so the general comments made earlier that high ratios are bullish and
low ratios are bearish still hold true. However, quantifying just what is "high"
and what is "low" leaves room for interpretation.
One school believes that absolute ratios should be used. An example might be:
"if the 10-day moving average of the equity put-call ratio is over 0.60, that is a buy
signal." Unfortunately, applying absolute figures to any of the ratios can be counter
productive at times. If the market is in the grip of a prolonged bearish move, more
and more puts will continue to be purchased, sending the ratio quite high before it
can reverse and start coming back to normal levels. Therefore, it is better to look for
the ratios to make a high or a low before calling a buy or sell signal. This is a more
dynamic interpretation; it allows for buy and sell signals to come at different absolute
levels of the put-call ratio.
Figure 29-1 shows the 50-day equity put-call ratio going back several years (the
daily figures for the previous 50 trading days are averaged to produce the number
plotted on the chart each day). One can see that at certain times, the put-call ratio
reached extreme heights before finally generating a buy signal. Attempting to call a
buy on the market at an absolute level would have been an error because the entry
point would have come too early. Notice that the readings in late 1990- as the mar
ket bottomed in advance of Operation Desert Storm - were actually higher on an
absolute basis than those made after the stock market crash in 1987. Similar obser
vations can be made for sell signals after the ratio has reached low levels: don't antic
ipate - wait for the ratio to bottom out and tum up before declaring a sell signal or
to roll over and turn down before declaring a buy signal.
The index put-call ratio is shown in Figure 29-2. It tells a similar story to the
equity ratio, although there are certainly differences - beyond the obvious one that
the ratios have different absolute values. Note that this ratio averages about 1.00
while the equity ratio averaged about 0.50.
At times, index put buying becomes extensive even as the market climbs. This
does not generally happen with equity options. It seems that institutional money
managers, who are long stocks, are afraid that they will lose their profits after a quick
stock market advance. However, rather than sell their stocks, they buy puts (possibly
overpaying for them). Thus, they are really bullish (they own stocks), but they are
buying puts as a hedge.
This is a difficult situation for the contrarian. What is the institutional manag
er's true bias? Is he bullish because he still owns stocks or is he bearish because he
is buying puts? This is the bane of contrary analysis - attempting to accurately inter
pret the data that is being received. Figure 29-2 shows that the index put-call ratio
Chapter 29: Introduction to Index Option Products and Futures 523
is less reliable than the equity ratio, but is still helpful in determining market tops
and bottoms.
In summary, the put-call ratio is an easily calculated one. Daily fluctuations can
be smoothed out into 10-, 20-, or 50-day moving averages. The ratio should be inter
preted bullishly when there is too much put buying and bearishly when there is too
much call buying. The phrase "too much" is not easily interpreted, but looking for
local maxima or local minima in the chart pattern is a reasonable way to approach the
problem. When the put-call ratio moving average is increasing, a buy signal would
not be given until the average rolls over and begins declining; a sell signal would be
generated when the average which is declining bottoms out.
SUMMARY
There are several kinds of indices and several kinds of trading vehicles: cash-based
options, futures options, and futures. These various underlying securities have dif
fering terms in the way they trade and also in the way their options are designed. This
variety creates many opportunities for astute option strategists.
524 Part V: Index Options and Futures
FIGURE 29-1.
50-day equity put-call ratio: 1985-2000.
100
90
R 80
a
~ 70 I
0
60
50
40
70 R .
a
t
i 60
0
\
\
MAMJJASONDJFMAMJJASONDJFMAMJ
1985 1986 Date
Put-Call Ratio
~JASONDJFMAMJJASONDJFMAMJJASO
1987 1988 1989 Date
Put-Call Ratio
Chapter 29: Introduction to Index Option Products and Futures
FIGURE 29-1.
{Continued)
110
100
90
R
r 80
i
0
70
60
I I ,,· /,,: ,. ~,., \ !
l \ .; , \ ; ,. / ....... i ,,,JV V
$SPX
300
50~+-+-+-+-+-lf-+-+--+-+-+-+-+--+-+-+-t--1-+-lf-+-t--+-+-1-1--+-t
90
R 80
a
t
i
o 70
NDJFMAMJJASONDJFMAMJJASONDJFM
1990 1991 Date
Put-Call Ratio
400
AMJJASONDJFMAMJJASONDJFMAMJJ
1992 1993 Date
Put-Call Ratio
525
526
FIGURE 29-1.
(Continued)
80
70
R 60
a
t
40
Part V: Index Options and Futures
500
ASONDJFMAMJJASONDJFMAMJJASON
1994 1995 1996 Date
Put-Call Ratio
110
100
90
R 80
a
t 70
0
60
50
""""
' ' ! \
1997 1998 Date
Put-Call Ratio
Chapter 29: Introduction to Index Option Products and Futures
FIGURE 29-1.
(Continued)
70
R 60
a
t
i
0
50
MJ JASONDJFMAMJ JASON
1999 2000 Date
Put-Call Ratio
FIGURE 29-2.
50-day index put-call ratio: 1985-91.
170 300
160
150
140 $SPX
130
R 120 200
a
t
0
90
80
70
60
50
MAMJJASONDJFMAMJJASONDJFMAMJ
1985 1986 Date
527
528 Part V: Index Options and Futures
FIGURE 29-2.
(Continued)
180
17