714 Part V: Index Options and Futures
calls more profitable than the loss in his puts. This is the advantage of using in-the
money options instead of futures in futures spreading strategies.
In fairness, it should be pointed out that if the futures prices had remained rel
atively unchanged, the 0.12 points of time value premium ($300) could have been
lost, while the futures spread may have been relatively unchanged. However, this
does not alter the reasoning behind wanting to use this option strategy.
Another consideration that might come into play is the margin required. Recall
that the initial margin for implementing the TED spread was $400. However, if one
uses the option strategy, he must pay for the options in full - $1,800 in the above
example. This could conceivably be adeterrent to using the option strategy. Of
course, if by investing $1,800, one can make money instead of losing money with the
smaller investment, then the initial margin requirement is irrelevant. Therefore, the
profit potential must be considered the more important factor.
FOLLOW-UP CONSIDERATIONS
When one uses long option combinations to implement afutures spread strategy, he
may find that his position changes from aspread to more of an outright position. This
would occur if the markets were volatile and one option became deeply in-the
money, while the other one was nearly worthless. The TED spread example above
showed how this could occur as the call wound up being worth 1.00, while the put
was virtually worthless.
As one side of the option spread goes out-of-the-money, the spread nature
begins to disappear and amore outright position takes its place. One can use the
deltas of the options in order to calculate just how much exposure he has at any one
time. The following examples go through aseries of analyses and trades that astrate
gist might have to face. The first example concerns establishing an intermarket
spread in oil products.
Example: In late summer, aspreader decides to implement an intermarket spread.
He projects that the coming winter may be severely cold; furthermore, he believes
that gasoline prices are too high, being artificially buoyed by the summer tourist sea
son, and the high prices are being carried into the future months by inefficient mar
ket pricing.
Therefore, he wants to buy heating oil futures or options and sell unleaded
gasoline futures or options. He plans to be out of the trade, if possible, by early
December, when the market should have discounted the facts about the winter.
Therefore, he decides to look at January futures and options. The following prices
exist:

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Chapter 35: Futures Option Strategies for Futures Spreads
Future or Option
January heating oil futures:
January unleaded gasoline futures:
January heating oil 60 call:
January unleaded gas 62 put:
Price
.6550
.5850
6.40
4.25
715
Time Value
Premium
0.90
0.75
The differential in futures prices is .07, or 7 cents per gallon. He thinks it could
grow to 12 cents or so by early winter. However, he also thinks that oil and oil prod
ucts have the potential to be very volatile, so he considers using the options. One cent
is worth $420 for each of these items.
The time value premium of the options is 1.65 for the put and call combined. If
he pays this amount ($693) per combination, he can still make money if the futures
widen by 5.00 points, as he expects. Moreover, the option spread gives him the
potential for profits if oil products are volatile, even if he is wrong about the futures
relationship.
Therefore, he decides to buy five combinations:
Position
Buy 5 January heating oil 60 calls @ 6.40
Buy 5 January unleaded 62 puts @ 4.25
Total cost:
Cost
$13,440
8,925
$22,365
This initial cost is substantially larger than the initial margin requirement for
five futures spreads, which would be about $7,000. Moreover, the option cost must
be paid for in cash, while the futures requirement could be taken care of with
Treasury bills, which continue to earn money for the spreader. Still, the strategist
believes that the option position has more potential, so he establishes it.
Notice that in this analysis, the strategist compared his time value premium cost
to the profit potential he expected from the futures spread itself This is often agood
way to evaluate whether or not to use options or futures. In this example, he thought
that, even if futures prices remained relatively unchanged, thereby wasting away his
time premium, he could still make money - as long as he was correct about heating
oil outperforming unleaded gasoline.
Some follow-up actions will now be examined. If the futures rally, the position
becomes long. Some profit might have accrued, but the whole position is subject to
losses if the futures fall in price. The strategist can calculate the extent to which his

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716 Part V: Index Options and Futures
position has become long by using the delta of the options in the strategy. He can
then use futures or other options in order to make the position more neutral, if he
wants to.
Example: Suppose that both unleaded gasoline and heating oil have rallied some and
that the futures spread has widened slightly. The following information is known:
Future or Option
January heating oil futures:
January unleaded gasoline futures:
January heating oil 60 call:
January unleaded gas 62 put:
Total profit:
Price
.7100
.6300
11.05
1.50
Net
Change
+ .055
+ .045
+ 4.65
- 2.75
Profit/loss
+$9,765
- 5,775
+$3,990
The futures spread has widened to 8 cents. If the strategist had established the
spread with futures, he would now have aone-cent ( $420) profit on five contracts, or
a $2,100 profit. The profit is larger in the option strategy.
The futures have rallied as well. Heating oil is up 5½ cents from its initial price,
while unleaded is up 4½ cents. This rally has been large enough to drive the puts out
of-the-money. When one has established the intermarket spread with options, and
the futures rally this much, the profit is usually greater from the option spread. Such
is the case in this example, as the option spread is ahead by almost $4,000.
This example shows the most desirable situation for the strategist who has
implemented the option spread. The futures rally enough to force the puts out-of
the-money, or alternatively fall far enough to force the calls to be out-of-the-money.
If this happens in advance of option expiration, one option will generally have almost
all of its time value premium disappear (the calls in the above example). The other
option, however, will still have some time value ( the puts in the example).
This represents an attractive situation. However, there is apotential negative,
and that is that the position is too long now. It is not really aspread anymore. If
futures should drop in price, the calls will lose value quickly. The puts will not gain
much, though, because they are out-of-the-money and will not adequately protect
the calls. At this juncture, the strategist has the choice of taking his profit - closing
the position - or making an adjustment to make the spread more neutral once again.
He could also do nothing, of course, but astrategist would normally want to protect
aprofit to some extent.

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Chapter 35: Futures Option Strategies for Futures Spreads 717
Example: The strategist decides that, since his goal was for the futures spread to
widen to 12 cents, he will not remove the position when the spread is only 8 cents,
as it is now. However, he wants to take some action to protect his current profit, while
still retaining the possibility to have the profit expand.
As afirst step, the equivalent futures position (EFP) is calculated. The pertinent
data is shown in Table 35-5.
TABLE 35-5.
EFP of long combination.
Future or Option
January heating oil futures:
January unleaded gasoline futures:
January heating oil 60 call: Long 5
January unleaded gas 62 put: Long 5
Price
.7100
.6300
11.05
1.50
Delta
0.99
-0.40
EFP
+4.95
-2.00
Total EFP: +2.95
Overall, the position is long the equivalent of about three futures contracts. The
position'sprofitability is mostly related to whether the futures rise or fall in price, not
to how the spread between heating oil futures and unleaded gas futures behaves.
The strategist could easily neutralize the long delta by selling three contracts.
This would leave room for more profits if prices continue to rise ( there are still two
extra long calls). It would also provide downside protection if prices suddenly drop,
since the 5 long puts plus the 3 short futures would offset any loss in the 5 in-the
money calls.
Which futures should the strategist short? That depends on how confident he is
in his original analysis of the intermarket spread widening. If he still thinks it will
widen further, then he should sell unleaded gasoline futures against the deeply in
the-money heating oil calls. This would give him an additional profit or loss opportu
nity based on the relationship of the two oil products. However, ifhe decides that the
intermarket spread should have widened more than this by now, perhaps he will just
sell 3 heating oil futures as adirect hedge against the heating oil calls.
Once one finds himself in aprofitable situation, as in the above example, the
rrwst conservative course is to hedge the in-the-rrwney option with its own underly
ing future. This action lessens the further dependency of the profits on the inter
market spread. There is still profit potential remaining from futures price action.
Furthermore, if the futures should fall so far that both options return to in-the
money status, then the intermarket spread comes back into play. Thus, in the above

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718 Part V: Index Options and Futures
example, the conservative action would be to sell three heating oil futures against the
heating oil calls.
The more aggressive course is to hedge the in-the-money option with the future
underlying the other side of the intermarket spread. In the above example, that
would entail selling the unleaded gasoline futures against the heating oil calls.
Suppose that the strategist in the previous example decides to take the conser
vative action, and he therefore shorts three heating oil futures at .7100, the current
price. This action preserves large profit potential in either direction. It is better than
selling out-of-the-money options against his current position.
He would consider removing the hedge if futures prices dropped, perhaps
when the puts returned to an in-the-money status with aput delta of at least -0. 75
or so. At that point, the position would be at its original status, more or less, except
for the fact that he would have taken anice profit in the three futures that were sold
and covered.
Epilogue. The above examples are taken from actual price movements. In reality,
the futures fell back, not only to their original price, but far below it. The funda
mental reason for this reversal was that the weather was warm, hurting demand for
heating oil, and gasoline supplies were low. By the option expiration in December,
the following prices existed:
January heating oil futures: .5200
January unleaded gas futures: .5200
Not only had the futures prices virtually crashed, but the intermarket spread
had been decimated as well. The spread had fallen to zero! It had never reached any
thing near the 12-cent potential that was envisioned. Any spreader who had estab
lished this spread with futures would almost certainly have lost money; he probably
would not have held it until it reached this lowly level, but there was never much
opportunity to get out at aprofit.
The strategist who established the spread with options, however, most certain
ly would have made money. One could safely assume that he covered the three
futures sold in the previous example at anice profit, possibly 7 points or so. One
could also assume that as the puts became in-the-money options, he established asimilar hedge and bought three unleaded gasoline futures when the EFP reached
-3.00. This probably occurred with unleaded gasoline futures around .5700-5 cents
in the money.
Assuming that these were the trades, the following table shows the profits and
losses.

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Chapter 35: Futures Option Strategies for Futures Spreads 719
Initial Final Net Profit/
Position Price Price Loss
Bought 5 calls 6.40 0 -$13,440
Bought 5 puts 4.25 10.00 + 12,075
Sold 3 heating oil futures .7100 .6400 + 8,820
Bought 3 unleaded gas futures .5700 .5200 - 6,300
Total profit: +$ 1,155
In the final analysis, the fact that the intermarket spread collapsed to zero actu
ally aided the option strategy, since the puts were the in-the-money option at expira
tion. This was not planned, of course, but by being long the options, the strategist was
able to make money when volatility appeared.
INTRAMARKET SPREAD STRATEGY
It should be obvious that the same strategy could be applied to an intramarket spread
as well. If one is thinking of spreading two different soybean futures, for example, he
could substitute in-the-money options for futures in the position. He would have the
same attributes as shown for the intermarket spread: large potential profits if volatil
ity occurs. Of course, he could still make money if the intramarket spread widens, but
he would lose the time value premium paid for the options.
SPREADING FUTURES AGAINST STOCK SECTOR INDICES
This concept can be carried one step further. Many futures contracts are related to
stocks - usually to asector of stocks dealing in aparticular commodity. For example,
there are crude oil futures and there is an Oil & Gas Sector Index (XOI). There are
gold futures and there is a Gold & Silver Index (XAU). If one charts the history of
the commodity versus the price of the stock sector, he can often find tradeable pat
terns in terms of the relationship between the two. That relationship can be traded
via an intermarket spread using options.
For example, if one thought crude oil was cheap with respect to the price of oil
stocks in general, he could buy calls on crude oil futures and buy puts on the Oil &
Gas (XOI) Index. One would have to be certain to determine the number of options
to trade on each side of the spread, by using the ratio that was presented in Chapter
31 on inter-index spreading. (In fact, this formula should be used for futures inter
market spreading if the two underlying futures don'thave the same terms.) Only now,
there is an extra component to add if options are used - the delta of the options:

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720 Part V: Index Options and Futures
where vi = volatility
Pi = price of the underlying
ui = unit of trading of the option
Lli = delta of the option
Example: Suppose that one indeed wants to buy crude oil calls and also buy puts on
the XOI Index because he thinks that crude oil is cheap with respect to oil stocks.
The following prices exist:
July crude futures: 16.35
Crude July 1550 call: 1.10
Volatility: 25%
Call delta: O. 7 4
$XOI: 256.50
June 265 put: 14½
Volatility: 17%
Put delta: 0. 73
The unit of trading for XOI options is $100 per point, as it is with nearly all stock and
index options. The unit of trading for crude oil futures and options is $1,000 per
point. With all of this information, the ratio can be computed:
Crude= 1,000 x 0.25 x 16.35 x 0.74
XOI = 100 x 0.17 x 256.50 x 0.73
Ratio = Crude/ XOI = 0.91
Therefore, one would buy 0.91 XOI put for every 1 crude oil call that he bought. For
small accounts, this is essentially a 1-to-lratio, but for large accounts, the exact ratio
could be used (for example, buy 91 XOI puts and 100 crude oil calls). The resultant
quantities encompass the various differences in these two markets - mainly the price
and volatility of the underlyings, plus the large differential in their units of trading
(100 vs. 1,000).
SUMMARY
Futures spreading is avery important and potentially profitable endeavor. Utilizing
options in these spreads can often improve profitability to the point that an originally
mistaken assumption can be overcome by volatility of price movement.

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Chapter 35: Futures Option Strategies for Futures Spreads 721
Futures spreads fall into two categories - intermarket and intramarket. They
are important strategies because many futures exhibit historic and/or seasonal ten
dencies that can be traded without regard to the overall movement of futures prices.
Options can be used to enhance these futures spreading strategies. The futures
calendar spread is closely related to the intramarket spread. It is distinctly different
from the stock or index option calendar spread.
Using in-the-money long option combinations in lieu of futures can be avery
attractive strategy for either intermarket or intramarket spreads. The option strategy
gives the spreader two ways to make money: ( 1) from the movement of the underly
ing futures in the spread; or (2) if the futures prices experience abig move, from the
fact that one option can continually increase in value while the other can drop only
to zero. The option strategy also affords the strategist the opportunity for follow-up
action based on the equivalent futures position that accumulates as prices rise or fall.
The concepts introduced in this chapter apply not only to futures spreads, but
to intermarket spreads between any two entities. An example was given of an inter
market spread between futures and astock sector index, but the concept can be gen
eralized to apply to any two related markets of any sort.
Traders who utilize futures spreads as part of their trading strategy should give
serious consideration to substituting options when applicable. Such an alternative
strategy will often improve the chances for profit.

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724 Part VI: Measuring and Trading Volatility
Even though amyriad of strategies and concepts have been presented so far, acom
mon thread among them is lacking. The one thing that ties all option strategies
together and allows one to make comparative decisions is volatility. In fact, volatility
is the most important concept in option trading. Oh, sure, if you're agreat picker of
stocks, then you might be able to get by without considering volatility. Even then,
though, you'dbe operating without full consideration of the main factor influencing
option prices and strategy. For the rest of us, it is mandatory that we consider volatil
ity carefully before deciding what strategy to use. In this section of the book, an
extensive treatment of volatility and volatility trading is presented. The first part
defines the terms and discusses some general concepts about how volatility can - and
should - be used. Then, anumber of the more popular strategies, described earlier
in the book, are discussed from the vantage point of how they perform when implied
volatilities change. After that, volatility trading strategies are discussed - and these
are some of the most important concepts for option traders. Adiscussion is present
ed of how stock prices actually behave, as opposed to how investors perceive them to
behave, and then specific criteria and methodology for both buying and selling
volatility are introduced.
The information to be presented here is not overly theoretical. All of the con
cepts should be understandable by most option traders. Whether or not one chooses
to actually "trade volatility," it is nevertheless important for an option trader to under
stand the concepts that underlie the basic principles of volatility trading.
WHY TRADE
11
THE MARKET"?
The "game" of stock market predicting holds appeal for many because one who can
do it seems powerful and intelligent. Everyone has his favorite indicators, analysis
techniques, or "black box" trading systems. But can the market really be predicted?
And if it can't, what does that say about the time spent trying to predict it? The
answers to these questions are not clear, and even if one were to prove that the mar
ket can'tbe predicted, most traders would refuse to believe it anyway. In fact, there
may be more than one way to "predict" the market, so in acertain sense one has to
qualify exactly what he is talking about before it can be determined if the market can
be predicted or not.
The astute option trader knows that market prediction falls into two categories:
(1) the prediction of the short-term movement of prices, and (2) the prediction of
volatility of the underlying. These are not independent predictions. For example,
anyone who is using a "target" is trying to predict both. That'spretty hard. Not only
do you have to be right about the direction of prices, but you also have to be able to

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CHAPTER 36
The Basics of
Volatility Trading
Volatility trading first attracted mathematically oriented traders who noticed that the
market'sprediction of forthcoming volatility - for example, implied volatility - was
substantially out of line with what one might reasonably expect should happen.
Moreover, many of these traders (market-makers, arbitrageurs, and others) had
found great difficulties with keeping a "delta neutral" position neutral. Seeking abet
ter way to trade without having amarket opinion on the underlying security, they
turned to volatility trading. This is not to suggest that volatility trading eliminates all
market risk, turning it all into volatility risk, for example. But it does suggest that acertain segment of the option trading population can handle the risk of volatility with
more deference and aplomb than they can handle price risk
Simply stated, it seems like amuch easier task to predict volatility than to pre
dict prices. That is said notwithstanding the great bull market of the 1990s, in which
every investor who strongly participated certainly feels that he understands how to
predict prices. Remember not to confuse brains with abull market. Consider the chart
in Figure 36-1. This seems as if it might be agood stock to trade: Buy it near the lows
and sell it near the highs, perhaps even selling it short near the highs and covering
when it later declines. It appears to have been in atrading range for along time, so
that after each purchase or sale, it returns at least to the midpoint of its trading range
and sometimes even continues on to the other side of the range. There is no scale on
the chart, but that doesn'tchange the fact that it appears to be atradable entity. In
fact, this is achart of implied volatility of the options on amajor U.S. corporation. It
really doesn'tmatter which one (it's IBM), because the implied volatility chart of near
ly every stock, index, or futures contract has asimilar pattern - atrading range. The
only time that implied volatility will totally break out of its "normal" range is if some
thing material happens to change the fundamentals of the way the stock moves - atakeover bid, for example, or perhaps amajor acquisition or other dilution of the stock
727

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728 Part VI: Measuring and Trading Volatility
FIGURE 36-1.
Asample chart.
Buy at these points.
So, many traders observed this pattern and have become adherents of trying to
predict volatility. Notice that if one is able to isolate volatility, he doesn'tcare where
the stock price goes he is just concerned with buying volatility near the bottom of
the range and selling it when it gets back to the middle or high end of the range, or
vice versa. In real life, it is nearly impossible for apublic customer to be able to iso
late volatility so specifically. He will have to pay some attention to the stock price, but
he still is able to establish positions in which the direction of the stock price is irrel
evant to the outcome of the position. This quality is appealing to many investors, who
have repeatedly found it difficult to predict stock prices. Moreover, an approach such
as this should work in both bull and bear markets. Thus, volatility trading appeals to
agreat number of individuals. Just remember that, for you personally to operate astrategy properly, you must find that it appeals to your own philosophy of trading.
Trying to use astrategy that you find uncomfortable will only lead to losses and frus
tration. So, if this somewhat neutral approach to option trading sounds interesting to
you, then read on.
DEFINITIONS OF VOLATILITY
Volatility is merely the term that is used to describe how fast astock, future, or index
changes in price. When one speaks of volatility in connection with options, there are
two types of volatility that are important. The first is historical volatility, which is ameasure of how fast the underlying instrument has been changing in price. The other
is implied volatility, which is the option market'sprediction of the volatility of the

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Chapter 36: The Basics of Volatility Trading 729
underlying over the life of the option. The computation and comparison of these two
measures can aid immensely in predicting the forthcoming volatility of the underly
ing instrument - acrucial matter in determining today'soption prices.
Historical volatility can be measured with aspecific formula, as shown in the ·
chapter on mathematical applications. It is merely the formula for standard deviation
as contained in most elementary books on statistics. The important point to under
stand is that it is an exact calculation, and there is little debate over how to compute
historical volatility. It is not important to know what the actual measurement means.
That is, if one says that acertain stock has ahistorical volatility of 20%, that by itself
is arelatively meaningless number to anyone but an ardent statistician. However, it
can be used for comparative purposes.
The standard deviation is expressed as apercent. One can determine that the
historical volatility of the broad stock market has usually been in the range of 15% to
20%. Avery volatile stock might have an historical volatility in excess of 100%. These
numbers can be compared to each other, so that one might say that astock with the
latter historical volatility is five times more volatile that the "stock market." So, the
historical volatility of one instrument can be compared with that of another instru
ment in order to determine which one is more volatile. That in itself is auseful func
tion of historical volatility, but its uses go much farther than that.
Historical volatility can be measured over different time periods to give one asense of how volatile the underlying has been over varying lengths of time. For exam
ple, it is common to compute a 10-day historical volatility, as well as a 20-day, 50-day,
and even 100-day. In each case, the results are annualized so that one can compare
the figures directly.
Consider the chart in Figure 36-2. It shows astock (although it could be afutures contract or index, too) that was meandering in arather tight range for quite
some time. At the point marked "A" on the chart, it was probably at its least volatile.
At that time, the 10-dayvolatility might have been something quite low, say 20%. The
price movements directly preceding point Ahad been very small. However, prior to
that time the stock had been more volatile, so longer-term measures of the historical
volatility would shown higher numbers. The possible measures of historical volatility,
then at point A, might have been something like:
10-day historical volatility: 20%
20-day historical volatility: 23%
50-day historical volatility: 35%
100-day historical volatility: 45%
Apattern of historical volatilities of this sort describes astock that has been
slowing down lately.

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730
FIGURE 36-2.
Sample stock chart.
:::::::::r;~.w· r
I
, .. ~
n
Ill•• ~N
IT
Part VI: Measuring and Trading Volatllity
:
I
Ijj
~
JI
• I'
'Vn ~- A
Its price movements have been less extreme in the near term.
Again referring to Figure 36-2, note that shortly after point A, the stock jumped
much higher over ashort period of time. Price action like this increases the implied
volatility dramatically. And, at the far right edge of the chart, the stock had stopped
rising but was swinging back and forth in far more rapid fashion than it had been at
most other points on the chart. Violent action in aback-and-forth manner can often
produce ahigher historical volatility reading that straight-line move can; it'sjust the
way the numbers work out. So, by the far right edge of the chart, the 10-day histori
cal volatility would have increased rather dramatically, while the longer-term meas
ures wouldn'tbe so high because they would still contain the price action that
occurred prior to point A.
At the far right edge of Figure 36-2, these figures might apply:
l 0-day historical volatility: 80%
20-day historical volatility: 75%
50-day historical volatility: 60%
l 00-day historical volatility: 55%
With this alignment of historical volatilities, one can see that the stock has been
more volatile recently than in the more distant past. In Chapter 38 on the distribu
tion of stock prices, we will discuss in some detail just which one, if any, of these his
torical volatilities one should use as "the" historical volatility input into option and

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Chapter 36: The Basics of Volatility Trading 731
probability models. We need to be able to make volatility estimates in order to deter
mine whether or not astrategy might be successful, and to determine whether the
current option price is arelatively cheap one or arelatively expensive one. For exam
ple, one can'tjust say, "Ithink XYZ is going to rise at least 18 points by February expi
ration." There needs to be some basis in fact for such astatement and, lacking inside
information about what the company might announce between now and February,
that basis should be statistics in the form of volatility projections.
Historical volatility is, of course, useful as an input to the (Black-Scholes) option
model. In fact, the volatility input to any model is crucial because the volatility com
ponent is such amajor factor in determining the price of an option. Furthermore,
historical volatility is useful for more than just estimating option prices. It is neces
sary for making stock price projections and calculating distributions, too, as will be
shown when those topics are discussed later. Any time one asks the question, "What
is the probability of the stock moving from here to there, or of exceeding aparticu
lar target price?" the answer is heavily dependent on the volatility of the underlying
stock (or index or futures).
It is obvious from the above example that historical volatility can change dra
matically for any particular instrument. Even if one were to stick with just one
measure of historical volatility ( the 20-day historical is commonly the most popular
measure), it changes with great frequency. Thus, one can never be certain that bas
ing option price predictions or stock price distributions on the current historical
volatility will yield the "correct" results. Statistical volatility may change as time
goes forward, in which case your projections would be incorrect. Thus, it is impor
tant to make projections that are on the conservative side.
ANOTHER APPROACH: GARCH
GARCH stands for Generalized Autoregressive Conditional Heteroskedasticity,
which is why it'sshortened to GARCH. It is atechnique for forecasting volatility that
some analysts say produces better projections than using historical volatility alone or
implied volatility alone. GARCH was created in the 1980s by specialists in the field of
econometrics. It incorporates both historical and implied volatility, plus one can throw
in aconstant ("fudge factor"). In essence, though, the user of GARCH volatility mod
els has to make some predictions or decisions about the weighting of the factors used
for the estimate. By its very nature, then, it can be just as vague as the situations
described in the previous section.
The model can "learn," though, if applied correctly. That is, if one makes avolatility prediction for today (using GARCH, let'ssay), but it turns out that the actu-

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732 Part VI: Measuring and Trading Volatility
al volatility was lower, then when you make the volatility prediction for tomorrow,
you'll probably want to adjust it downward, using the experience of the real world,
where you see volatility declining. This also incorporates the common-sense notion
that volatility tends to remain the same; that is, tomorrow'svolatility is likely to be
much like today's. Of course, that'salittle bit like saying tomorrow'sweather is likely
to be the same as today's (which it is, two-thirds of the time, according to statistics).
It'sjust that when atornado hits, you have to realize that your forecast could be wrong.
The same thing applies to GAR CH volatility projections. They can be wrong, too.
So, GARCH does not do aperfect job of estimating and forecasting volatility. In
fact, it might not even be superior, from astrategist'sviewpoint, to using the simple
minimum/maximum techniques outlined in the previous section. It is really best
geared to predicting short-term volatility and is favored most heavily by dealers in
currency options who must adjust their markets constantly. For longer-term volatility
projections, which is what aposition trader of volatility is interested in, GARCH may
not be all that useful. However, it is considered state-of-the-art as far as volatility pre
dicting goes, so it has afollowing among theoretically oriented traders and analysts.
MOVING AVERAGES
Some traders try to use moving averages of daily composite implied volatility read
ings, or use asmoothing of recent past historical volatility readings to make volatility
estimates. As mentioned in the chapter on mathematical applications, once the com
posite daily implied volatility has been computed, it was recommended that asmoothing effect be obtained by taking amoving average of the 20 or 30 days'
implied volatilities. In fact, an exponential moving average was recommended,
because it does not require one to keep accessing the last 20 or 30 days' worth of data
in order to compute the moving average. Rather, the most recent exponential mov
ing average is all that'sneeded in order to compute the next one.
IMPLIED VOLATILITY
Implied volatility has been mentioned many times already, but we want to expand on
its concept before getting deeper into its measure and uses later in this section.
Implied volatility pertains only to options, although one can aggregate the implied
volatilities of the various options trading on aparticular underlying instrument to
produce asingle number, which is often referred to as the implied volatility of the
underlying.

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732 Part VI: Measuring and Trading Volatility
al volatility was lower, then when you make the volatility prediction for tomorrow,
you'll probably want to adjust it downward, using the experience of the real world,
where you see volatility declining. This also incorporates the common-sense notion
that volatility tends to remain the same; that is, tomorrow'svolatility is likely to be
much like today's. Of course, that'salittle bit like saying tomorrow'sweather is likely
to be the same as today's (which it is, two-thirds of the time, according to statistics).
It'sjust that when atornado hits, you have to realize that your forecast could be wrong.
The same thing applies to GARCH volatility projections. They can be wrong, too.
So, GARCH does not do aperfect job of estimating and forecasting volatility. In
fact, it might not even be superior, from astrategist'sviewpoint, to using the simple
minimum/maximum techniques outlined in the previous section. It is really best
geared to predicting short-term volatility and is favored most heavily by dealers in
currency options who must adjust their markets constantly. For longer-term volatility
projections, which is what aposition trader of volatility is interested in, GAR CH may
not be all that useful. However, it is considered state-of-the-art as far as volatility pre
dicting goes, so it has afollowing among theoretically oriented traders and analysts.
MOVING AVERAGES
Some traders try to use moving averages of daily composite implied volatility read
ings, or use asmoothing of recent past historical volatility readings to make volatility
estimates. As mentioned in the chapter on mathematical applications, once the com
posite daily implied volatility has been computed, it was recommended that asmoothing effect be obtained by taking amoving average of the 20 or 30 days'
implied volatilities. In fact, an exponential moving average was recommended,
because it does not require one to keep accessing the last 20 or 30 days' worth of data
in order to compute the moving average. Rather, the most recent exponential mov
ing average is all that'sneeded in order to compute the next one.
IMPLIED VOLATILITY
Implied volatility has been mentioned many times already, but we want to expand on
its concept before getting deeper into its measure and uses later in this section.
Implied volatility pertains only to options, although one can aggregate the implied
volatilities of the various options trading on aparticular underlying instrument to
produce asingle number, which is often referred to as the implied volatility of the
underlying.

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732 Part VI: Measuring and Trading Volatility
al volatility was lower, then when you make the volatility prediction for tomorrow,
you'll probably want to adjust it downward, using the experience of the real world,
where you see volatility declining. This also incorporates the common-sense notion
that volatility tends to remain the same; that is, tomorrow'svolatility is likely to be
much like today's. Of course, that'salittle bit like saying tomorrow'sweather is likely
to be the same as today's (which it is, two-thirds of the time, according to statistics).
It'sjust that when atornado hits, you have to realize that your forecast could be wrong.
The same thing applies to GARCH volatility projections. They can be wrong, too.
So, GAR CH does not do aperfect job of estimating and forecasting volatility. In
fact, it might not even be superior, from astrategist'sviewpoint, to using the simple
minimum/maximum techniques outlined in the previous section. It is really best
geared to predicting short-term volatility and is favored most heavily by dealers in
currency options who must adjust their markets constantly. For longer-term volatility
projections, which is what aposition trader of volatility is interested in, GARCH may
not be all that useful. However, it is considered state-of-the-art as far as volatility pre
dicting goes, so it has afollowing among theoretically oriented traders and analysts.
MOVING AVERAGES
Some traders try to use moving averages of daily composite implied volatility read
ings, or use asmoothing of recent past historical volatility readings to make volatility
estimates. As mentioned in the chapter on mathematical applications, once the com
posite daily implied volatility has been computed, it was recommended that asmoothing effect be obtained by taking amoving average of the 20 or 30 days'
implied volatilities. In fact, an exponential moving average was recommended,
because it does not require one to keep accessing the last 20 or 30 days' worth of data
in order to compute the moving average. Rather, the most recent exponential mov
ing average is all that'sneeded in order to compute the next one.
IMPLIED VOLATILITY
Implied volatility has been mentioned many times already, but we want to expand on
its concept before getting deeper into its measure and uses later in this section.
Implied volatility pertains only to options, although one can aggregate the implied
volatilities of the various options trading on aparticular underlying instrument to
produce asingle number, which is often referred to as the implied volatility of the
underlying.

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Chapter 36: The Basics of Volatility Trading 733
At any one point in time, atrader knows for certain the following items that
affect an option'sprice: stock price, strike price, time to expiration, interest rate, and
dividends. The only remaining factor is volatility - in fact, implied volatility. It is the
big "fudge factor" in option trading. If implied volatility is too high, options will be
overpriced. That is, they will be relatively expensive. On the other hand, if implied
volatility is too low, options will be cheap or underpriced. The terms "overpriced" and
"underpriced" are not really used by theoretical option traders much anymore,
because their usage implies that one knows what the option should be worth. In the
modem vernacular, one would say that the options are trading with a "high implied
volatility" or a "low implied volatility," meaning that one has some sense of where
implied volatility has been in the past, and the current measure is thus high or low in
comparison.
Essentially, implied volatility is the option market'sguess at the forthcoming sta
tistical volatility of the underlying over the life of the option in question. If traders
believe that the underlying will be volatile over the life of the option, then they will
bid up the option, making it more highly priced. Conversely, if traders envision anon
volatile period for the stock, they will not pay up for the option, preferring to bid
lower; hence the option will be relatively low-priced. The important thing to note is
that traders normally do not know the future. They have no way of knowing, for sure,
how volatile the underlying is going to be during the life of the option.
Having said that, it would be unrealistic to assume that inside information does
not leak into the marketplace. That is, if certain people possess nonpublic knowledge
about acompany'searnings, new product announcement, takeover bid, and so on,
they will aggressively buy or bid for the options and that will increase implied volatil
ity. So, in certain cases, when one sees that implied volatility has shot up quickly, it is
perhaps asignal that some traders do indeed know the future - at least with respect
to aspecific corporate announcement that is about to be made.
However, most of the time there is not anyone trading with inside information.
Yet, every option trader - market-maker and public alike - is forced to make a
"guess" about volatility when he buys or sells an option. That is true because the price
he pays is heavily influenced by his volatility estimate ( whether or not he realizes that
he is, in fact, making such avolatility estimate). As you might imagine, most traders
have no idea what volatility is going to be during the life of the option. They just pay
prices that seem to make sense, perhaps based on historic volatility. Consequently,
today'simplied volatility may bear no resemblance to the actual statistical volatility
that later unfolds during the life of the option.
For those who desire amore mathematical definition of implied volatility, con
sider this.

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734 Part VI: Measuring and Trading Volatillty
Opt price = f(Stock price, Strike price, Time, Risk-free rate, Volatility, Dividends)
Furthermore, suppose that one knows the following information:
XYZ price: 52
April 50 call price: 6
Time remaining to April expiration: 36 days
Dividends: $0.00
Risk-free interest rate: 5%
This information, which is available for every option at any time, simply from an
option quote, gives us everything except the implied volatility. So what volatility
would one have to plug in the Black-Scholes model ( or whatever model one is using)
to make the model give the answer 6 (the current price of the option)? That is, what
volatility is necessary to solve the equation?
6 = f(52, 50, 36 days, 5%, Volatility, $0.00)
Whatever volatility is necessary to make the model yield the current market price (6)
as its value, is the implied volatility for the XYZ April 50 call. In this case, if you're
interested, the implied volatility is 75.4%. The actual process of determining implied
volatility is an iterative one. There is no formula, per se. Rather, one keeps trying var
ious volatility estimates in the model until the answer is close enough to the market
value.
THE VOLATILITY OF VOLATILITY
In order to discuss the implied volatility of aparticular entity - stock, index, or
futures contract one generally refers to the implied volatility of individual options
or perhaps the composite implied volatility of the entire option series. This is gener
ally good enough for strategic comparisons. However, it turns out that there might be
other ways to consider looking at implied volatility. In paiticular, one might want to
consider how wide the range of implied volatility is - that is, how volatile the indi
vidual implied volatility numbers are.
It is often conventional to talk about the percentile of implied volatility. That is
away to rank the current implied volatility reading with past readings for the same
underlying instrument.
However, afairly important ingredient is missing when percentiles are involved.
One can'treally tell if "cheap" options are cheap as apractical matter. That'sbecause
one doesn'tknow how tightly packed together the past implied volatility readings are.
For example, if one were to discover that the entire past range of implied volatility
for XYZ stretched only from 39% to 45%, then acurrent reading of 40%, while low,

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Chapter 36: The Basics of Volatility Trading 135
might not seem all that attractive. That is, if the first percentile of XYZ options were
at an implied volatility reading of 39% and the 100th percentile were at 45%, then areading of 40% is really quite mundane. There just wouldn'tbe much room for
implied volatility to increase on an absolute basis. Even if it rose to the 100th per
centile, an individual XYZ option wouldn'tgain much value, because its implied
volatility would only be increasing from about 40% to 45%.
However, if the distribution of past implied volatility is wide, then one can truly
say the options are cheap if they are currently in alow percentile. Suppose, rather
than the tight range described above, that the range of past implied volatilities for
XYZ instead stretched from 35% to 90% - that the first percentile for XYZ implied
volatility was at 35% and the 100th percentile was at 90%. Now, if the current read
ing is 40%, there is alarge range above the current reading into which the options
could trade, thereby potentially increasing the value of the options if implied volatil
ity moved up to the higher percentiles.
What this means, as apractical matter, is that one not only needs to know the
current percentile of implied volatility, but he also needs to know the range of num
bers over which that percentile was derived. If the range is wide, then an extreme
percentile truly represents acheap or expensive option. But if the range is tight, then
one should probably not be overly concerned with the current percentile of implied
volatility.
Another facet of implied volatility that is often overlooked is how it ranges with
respect to the time left in the option. This is particularly important for traders of
LEAPS (long-term) options, for the range of implied volatility of a LEAPS option will
not be as great as that of ashort-term option. In order to demonstrate this, the
implied volatilities of $OEX options, both regular and LEAPS, were charted over
several years. The resulting scatter diagram is shown in Figure 36-3.
Two curved lines are drawn on Figure 36-3. They contain most of the data
points. One can see from these lines that the range of implied volatility for near-term
options is greater than it is for longer-term options. For example, the implied volatil
ity readings on the far left of the scatter diagram range from about 14% to nearly 40%
(ignore the one outlying point). However, for longer-term options of 24 months or
more, the range is about 17% to 32%. While $0EX options have their own idiosyn
cracies, this scatter diagram is fairly typical of what we would see for any stock or
index option.
One conclusion that we can draw from this is that LEAPS option implied
volatilities just don'tchange nearly as much as those of short-term options. That can
be an important piece of information for a LEAPS option trader especially if he is
comparing the LEAPS implied volatility with acomposite implied volatility or with
the historical volatility of the underlying.

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736 Part VI: Measuring and Trading Volatility
Once again, consider Figure 36-3. While it is difficult to discern from the graph
alone, the 10th percentile of $OEX composite implied volatility, using all of the data
points given, is 17%. The line that marks this level (the tenth percentile) is noted on
the right side of the scatter diagram. It is quite easy to see that the LEAPS options
rarely trade at that low volatility level.
In Figure 36-3, the distance between the curved lines is much greater on the
left side (i.e., for shorter-term options) than it is on the right side (for longer-term
options). Thus, it'sdifficult for the longer-term options to register either an extreme
ly high or extremely low implied volatility reading, when all of the options are con
sidered. Consequently, LEAPS options will rarely appear "cheap" when one looks at
their percentile of implied volatility, including all the short-term options, too:
One might say that, if he were going to buy long-term options, he should look
only at the size of the volatility range on the right side of the scatter diagram. Then,
he could make his decision about whether the options are cheap or not by only com
paring the current reading to past readings of long-term options. This line of think
ing, though, is somewhat fallacious reasoning, for acouple of reasons: First, if one
holds the option for any long period of time, the volatility range will widen out and
there is achance that implied volatility could drop substantially. Second, the long
term volatility range might be so small that, even though the options are initially
cheap, quick increase in implied volatility over several deciles might not translate into
much of again in price in the short term.
FIGURE 36-3. Implied volatilities of $OEX options over several
years.
50
45
40
~ 35
~ 30
g 25 "O
.91 20 C.
E 15 -0th
10
5
0
0 10 20 30 40
Time to Expiration (months)

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Chapter 36: The Basics ol Volatility Trading 737
It'simportant for anyone using implied volatility in his trading decisions to
understand that the range of past implied volatilities is important, and to realize that
the volatility range expands as time shrinks.
IS IMPLIED VOLATILITY A GOOD PREDICTOR OF ACTUAL VOLATILITY?
The fact that one can calculate implied volatility does not mean that the calculation
is agood estimate of forthcoming volatility. As stated above, the marketplace does not
really know how volatile an instrument is going to be, any more than it knows the
forthcoming price of the stock. There are clues, of course, and some general ways of
estimating forthcoming volatility, but the fact remains that sometimes options trade
with an implied volatility that is quite abit out of line with past levels. Therefore,
implied volatility may be considered to be an inaccurate estimate of what is really
going to happen to the stock during the life of the option. Just remember that implied
volatility is aforward-looking estimate, and since it is based on traders' suppositions,
it can be wrong - just as any estimate of future events can be in error.
The question posed above is one that should probably be asked more often than
it is: "Is implied volatility agood predictor of actual volatility?" Somehow, it seems
logical to assume that implied and historical (actual) volatility will converge. That'snot really true, at least not in the short term. Moreover, even if they do converge,
which one was right to begin with - implied or historical? That is, did implied volatil
ity move to get more in line with actual movements of the underlying, or did the
stock'smovement speed up or slow down to get in line with implied volatility?
To illustrate this concept, afew charts will be used that show the comparison
between implied and historical volatility. Figure 36-4 shows information for the
$0EX Index. In general, $0EX options are overpriced. See the discussion in
Chapter 29. That is, implied volatility of $0EX options is almost always higher than
what actual volatility turns out to be. Consider Figure 36-4. There are three lines in
the figure: (a) implied volatility, (b) actual volatility, and (c) the difference between
the two. There is an important distinction here, though, as to what comprises these
curves:
(a) The implied volatility curve depicts the 20-day moving average of daily compos
ite implied volatility readings for $0EX. That is, each day one number is com
puted as acomposite implied volatility for $0EX for that day. These implied
volatility figures are computed using the averaging formula shown in the chapter
on mathematical applications, whereby each option'simplied volatility is weight
ed by trading volume and by distance in- or out-of-the-money, to arrive at asin
gle composite implied volatility reading for the trading day. To smooth out those
daily readings, a 20-day simple moving average is used. This daily implied volatil-

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738 Part VI: Measuring and Trading Volatility
FIGURE 36-4.
$OEX implied versus historical volatility.
10
Implied minus Actual 1999 Date
ity of $OEX options encompasses all the $OEX options, so it is different from the
Volatility Index ($VIX), which uses only the options closest to the money. By
using all of the options, aslightly different volatility figure is arrived at, as com
pared to $VIX, but achart of the two would show similar patterns. That is, peaks
in implied volatility computed using all of the $OEX options occur at the same
points in time as peaks in $VIX.
(b) The actual volatility on the graph is alittle different from what one normally
thinks of as historical volatility. It is the 20-day historical volatility, computed 20
days later than the date of the implied volatility calculation. Hence, points on the
implied volatility curve are matched with a 20-day historical volatility calculation
that was made 20 days later. Thus, the two curves more or less show the predic
tion of volatility and what actually happened over the 20-day period. These actu
al volatility readings are smoothed as well, with a 20-day moving average.
(c) The difference between the two is quite simple, and is shown as the bottom
curve on the graph. A "zero" line is drawn through the difference.
When this "difference line" passes through the zero line, the projection of
volatility and what actually occurred 20 days later were equal. If the difference line
is above the zero line, then implied volatility was too high; the options were over
priced. Conversely, if the difference line is below the zero line, then actual volatility
turned out to be greater than implied volatility had anticipated. The options were
underpriced in that case. Those latter areas are shaded in Figure 36-4. Simplistically,
you would want to own options during the shaded periods on the chart, and would
want to be aseller of options during the non-shaded areas.

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Chapter 36: The Basics of Volatility Trading 739
Note that Figure 36-4 indeed confirms the fact that $OEX options are consis
tently overpriced. Very few charts are as one-dimensional as the $OEX chart, where
the options were so consistently overpriced. Most stocks find the difference line
oscillating back and forth about the zero mark. Consider Figures 36-5 and 36-6.
Figure 36-5 shows achart similar to Figure 36-4, comparing actual and implied
volatility, and their difference, for aparticular stock. Figure 36-6 shows the price
graph of that same stock, overlaid on implied volatility, during the period up to and
including the heavy shading.
The volatility comparison chart (Figure 36-5) shows several shaded areas, dur
ing which the stock was more volatile than the options had predicted. Owners of
options profited during these times, provided they had amore or less neutral outlook
on the stock. Figure 36-6 shows the stock'sperformance up to and including the
March-April 1999 period - the largest shaded area on the chart. Note that implied
volatility was quite low before the stock made the strong move from 10 to 30 in little
more than amonth. These graphs are taken from actual data and demonstrate just
how badly out of line implied volatility can be. In February and early March 1999,
implied volatility was at or near the lowest levels on these charts. Yet, by the end of
March, amajor price explosion had begun in the stock, one that tripled its value in
just over amonth. Clearly, implied volatility was apoor predictor of forthcoming
actual volatility in this case.
What about later in the year? In Figure 36-5, one can observe that implied and
actual volatility oscillated back and forth quite afew times during the rest of 1999. It
might appear that these oscillations are small and that implied volatility was actually
doing apretty good job of predicting actual volatility, at least until the final spike in
December 1999. However, looking at the scale on the left-hand side of Figure 36-5,
one can see that implied volatility was trying to remain in the 50% to 60% range, but
actual volatility kept bolting higher rather frequently.
One more example will be presented. Figures 36-7 and 36-8 depict another
stock and its volatilities. On the left half of each graph, implied volatility was quite
high. It was higher than actual volatility turned out to be, so the difference line in
Figure 36-7 remains above the zero line for several months. Then, for some reason,
the option market decided to make an adjustment, and implied volatility began to
drop. Its lowest daily point is marked with acircle in Figure 36-8, and the same point
in time is marked with asimilar circle in Figure 36-7. At that time, options traders
were "saying" that they expected the stock to be very tame over the ensuing weeks.
Instead, the stock made two quick moves, one from 15 down to 11, and then anoth
er back up to 17. That movement jerked actual volatility higher, but implied volatili
ty remained rather low. After aperiod of trading between 13 and 15, during which
time implied volatility remained low, the stock finally exploded to the upside, as evi
denced by the spikes on the right-hand side of both Figures 36-7 and 36-8. Thus,

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742 Part VI: Measuring and Trading Volatility
implied volatility was apoor predictor of actual volatility for most of the time on these
graphs. Moreover, implied volatility remained low at the right-hand side of the charts
(January 2000) even though the stock doubled in the course of amonth.
The important thing to note from these figures is that they clearly show that
implied volatility is really not avery good predictor of the actual volatility that is to
follow. If it were, the difference line would hover near zero most of the time. Instead,
it swings back and forth wildly, with implied volatility over- or underestimating actu
al volatility by quite wide levels. Thus, the current estimates of volatility by traders
(i.e., implied volatility) can actually be quite wrong.
Conversely, one could also say that historical volatility is not agreat predictor of
volatility that is to follow, either, especially in the short term. No one really makes any
claims that it is agood predictor, for historical volatility is merely areflection of what
has happened in the past. All we can say for sure is that implied and historical volatil
ity tend to trade within arange.
One thing that does stand out on these charts is that implied volatility seems to
fluctuate less than actual volatility. That seems to be anatural function of the volatil
ity predictive process. For example, when the market collapses, implied volatilities of
options rise only modestly. This can be observed by again referring to Figure 36-4,
the $0EX option example. The only shaded area on the graph occurred when the
market had arather sharp sell-off during October 1999. In previous years, when
there had been even more severe market declines (October 1997 or August-October
1998) $0EX actual volatility had briefly moved above implied volatility (this data for
1997 and 1998 is shown in Figure 36-9). In other words, option traders and market
makers are predicting volatility when they price options, and one tends to make a
FIGURE 36-9.
$OEX implied versus historical volatility, 1997-1998.
Actual
40
30
10
0
D J F M A
-20 1997 1998

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Chapter 36: The Basics of Volatility Trading 743
prediction that is somewhat "middle of the road," since an extreme prediction is
more likely to be wrong. Of course, it turns out to be wrong anyway, since actual
volatility jumps around quite rapidly.
The few charts that have been presented here don'tconstitute arigorous study
upon which to draw the conclusion that implied volatility is apoor predictor of actu
al volatility, but it is this author'sfirm opinion that that statement is true. Agraduate
student looking for amaster'sthesis topic could take it from here.
VOLATILITY TRADING
As aresult of the fact that implied volatility can sometimes be at irrational extremes,
options may sometimes trade with implied volatilities that are significantly out of line
with what one would normally expect. For example, suppose astock is in arelatively
nonvolatile period, like the price of the stock in Figure 36-2, just before point Aon
the graph. During that time, option sellers would probably become more aggressive
while option buyers, who probably have been seeing their previous purchases decay
ing with time, become more timid. As aresult, option prices drop. Alternatively stat
ed, implied volatility drops. When implied volatilities are decreasing, option sellers
are generally happy (and may often become more aggressive), while option buyers
are losing money (and may often tend to become more timid). This is just afunction
of looking at the profit and loss statements in one'soption account. But anyone who
took alonger backward look at the volatility of the stock in Figure 36-2 would see that
it had been much more volatile in the past. Consequently, he might decide that the
implied volatility of the options had gotten too low and he would be abuyer of
options.
It is the volatility trader'sobjective to spot situations when implied volatility is
possibly or probably erroneous and to take aposition that would profit when the
error is brought to light. Thus, the volatility trader'smain objective is spotting situa
tions when implied volatility is overvalued or undervalued, irrespective of his outlook
for the underlying stock itself. In some ways, this is not so different from the funda
mental stock analyst who is attempting to spot overvalued or undervalued stocks,
based on earnings and other fundamentals.
From another viewpoint, volatility trading is also acontrarian theory of invest
ing. That is, when everyone else thinks the underlying is going to be nonvolatile, the
volatility trader buys volatility. When everyone else is selling options and option buy
ers are hard to find, the volatility trader steps up to buy options. Of course, some rig
orous analysis must be done before the volatility trader can establish new positions,
but when those situations come to light, it is most likely that he is taking positions
opposite to what "the masses" are doing. He will be buying volatility when the major-

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744 Part VI: Measuring and Trading Volatility
ity has been selling it (or at least, when the majority is refusing to buy it), and he will
be selling volatility when everyone else is panicking to buy options, making them
quite expensive.
WHY DOES VOLATILITY REACH EXTREMES?
One can'tjust buy every option that he considers to be cheap. There must be some
consideration given to what the probabilities of stock movement are. Even more
important, one can'tjust sell every option that he values as expensive. There may be
valid reasons why options become expensive, not the least of which is that someone
may have inside information about some forthcoming corporate news (atakeover or
an earnings surprise, for example).
Since options off er agood deal of leverage, they are an attractive vehicle to any
one who wants to make aquick trade, especially if that person believes he knows
something that the general public doesn'tknow. Thus, if there is aleak of atakeover
rumor - whether it be from corporate officers, investment bankers, printers, or
accountants - whoever possesses that information may quite likely buy options
aggressively, or at least bid for them. Whenever demand for an option outstrips sup
ply - in this case, the major supplier is probably the market-maker - the options
quickly get more expensive. That is, implied volatility increases.
In fact, there are financial analysts and reporters who look for large increases in
trading volume as aclue to which stocks might be ready to make abig move.
Invariably, if the trading volume has increased and if implied volatility has increased
as well, it is agood warning sign that someone with inside information is buying the
options. In such acase, it might not be agood idea to sell volatility, even though the
options are mathematically expensive.
Sometimes, even more minor news items are known in advance by asmall seg
ment of the investing community. If those items will be enough to move the stock
even acouple of points, those who possess the information may try to buy options in
advance of the news. Such minor news items might include the resignation or firing
of ahigh-ranking corporate officer, or perhaps some strategic alliance with another
company, or even anew product announcement.
The seller of volatility can watch for two things as warning signs that perhaps
the options are "predicting" acorporate event (and hence should be avoided as a
"volatility sale"). Those two things are adramatic increase in option volume or asud
den jump in implied volatility of the options. One or both can be caused by traders
with inside information trying to obtain aleveraged instrument in advance of the
actual corporate news item being made public.

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Chapter 36: The Basics of Volatility Trading 745
A SUDDEN INCREASE IN OPTION VOLUME OR IMPLIED VOLATILITY
The symptoms of insider trading, as evidenced by alarge increase in option trading
activity, can be recognized. Typically, the majority of the increased volume occurs in
the near-term option series, particularly the at-the-money strike and perhaps the next
strike out-of-the-money. The activity doesn'tcease there, however. It propagates out
to other option series as market-makers (who by the nature of their job function are
short the near-term options that those with insider knowledge are buying) snap up
everything on the books that they can find. In addition, the market-makers may try
to entice others, perhaps institutions, to sell some expensive calls against aportion of
their institutional stock holdings. Activity of this sort should be awarning sign to the
volatility seller to stand aside in this situation.
Of course, on any given day there are many stocks whose options are extraordi
narily active, but the increase in activity doesn'thave anything to do with insider trad
ing. This might include alarge covered call write or maybe alarge put purchase
established by an institution as ahedge against an existing stock position, or arela
tively large conversion or reversal arbitrage established by an arbitrageur, or even alarge spread transaction initiated by ahedge fund. In any of these cases, option vol
ume would jump dramatically, but it wouldn'tmean that anyone had inside knowl
edge about aforthcoming corporate event. Rather, the increases in option trading
volume as described in this paragraph are merely functions of the normal workings
of the marketplace.
What distinguishes these arbitrage and hedging activities from the machina
tions of insider trading is: (1) There is little propagation of option volume into other
series in the "benign" case, and (2) the stock price itself may languish. However,
when true insider activity is present, the market-makers react to the aggressive
nature of the call buying. These market-makers know they need to hedge themselves,
because they do not want to be short naked call options in case atakeover bid or
some other news spurs the stock dramatically higher. As mentioned earlier, they try
to buy up any other options offered in "the book," but there may not be many of
those. So, as alast result, the way they reduce their negative position delta is to buy
stock. Thus, if the options are active and expensive, and if the stock is rising too, you
probably have areasonably good indication that "someone knows something."
However, if the options are expensive but none of the other factors are present, espe
cially if the stock is declining in price - then one might feel more comfortable with astrategy of selling volatility in this case.
However, there is acase in which options might be the object of pursuit by
someone with insider knowledge, yet not be accompanied by heavy trading volume.
This situation could occur with illiquid options. In this case, afloor broker holding

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746 Part VI: Measuring and Trading Volatility
the order of those with insider information might come into the pit to buy options,
but the market-makers may not sell them many, preferring to raise their offering
price rather than sell alarge quantity. If this happens afew times in arow, the options
will have gotten very expensive as the floor broker raises his bid price repeatedly, but
only buys afew contracts each time. Meanwhile, the market-maker keeps raising his
offering price.
Eventually, the floor broker concludes that the options are too expensive to
bother with and walks away. Perhaps his client then buys stock. In any case, what has
happened is that the options have gotten very expensive as the bids and offers were
repeatedly raised, but not much option volume was actually traded because of the
illiquidity of the contracts. Hence the normal warning light associated with asudden
increase in option volume would not be present. In this case, though, avolatility sell
er should still be careful, because he does not want to step in to sell calls right before
some major corporate news item is released. The clue here is that implied volatility
literally exploded in ashort period of time (one day, or actually less time), and that
alone should be enough warning to avolatility seller.
The point that should be taken here is that when options suddenly become very
expensive, especially if accompanied by strong stock price movement and strong
stock volume, there may very well be agood reason why that is happening. That rea
son will probably become public knowledge shortly in the form of anews event. In
fact, amajor market-maker once said he believed that rrwst increases in implied
volatility were eventually justified - that is, some corporate news item was released
that made the stock jump. Hence, avolatility seller should avoid situations such as
these. Any sudden increase in implied volatility should probably be viewed as apotential news story in the making. These situations are not what aneutral volatility
seller wants to get into.
On the other hand, if options have become expensive as aresult of corporate
news, then the volatility seller can feel more comfortable making atrade. Perhaps the
company has announced poor earnings and the stock has taken abeating while
implied volatility rose. In this situation, one can assess the information and analyze it
clearly; he is not dealing with some hidden facts known to only afew insider traders.
With clear analysis, one might be able to develop avolatility selling strategy that is
prudent and potentially profitable.
Another situation in which options become expensive in the wake of market
action is during abear market in the underlying. This can be true for indices, stocks,
and futures contracts. The Crash of '87 is an extreme example, but implied volatility
shot through the roof during the crash. Other similar sharp market collapses - such
as October 1989, October 1997, and August-September 1998 - caused implied
volatility to jump dramatically. In these situations, the volatility seller knows why

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Chapter 31,: 1be Basics of Volatility Trading 747
implied volatility is high. Given that fact, he can then construct positions around aneutral strategy or around his view of the future. The time when the volatility seller
must be careful is when the options are expensive and no one seems to know why.
That'swhen insider trading may be present, and that'swhen the volatility seller
should defer from selling options.
CHEAP OPTIONS
When options are cheap, there are usually far less discernible reasons why they have
become cheap. An obvious one may be that the corporate structure of the company
has changed; perhaps it is being taken over, or perhaps the company· has acquired
another company nearly its size. In either case, it is possible that the combined enti
ty'sstock will be less volatile than the original company'sstock was. As the takeover
is in the process of being consummated, the implied volatility of the company'soptions will drop, giving the false impression that they are cheap.
In asimilar vein, acompany may mature, perhaps issuing more shares of stock,
or perhaps building such a.., good earnings stream that the stock is considered less
volatile than it formerly was. Some of the Internet companies will be classic cases: In
the beginning they were high-flying stocks with plenty of price movement, so the
options traded with arelatively high degree of implied volatility. However, as the com
pany matures, it buys other Internet companies and then perhaps even merges with alarge, established company (America Online and Time-Warner Communications, for
example). In these cases, actual (statistical) volatility will diminish as the company
matures, and implied volatility will do the same. On the surface, abuyer of volatility
may see the reduced volatility as an attractive buying situation, but upon further
inspection he may find that it is justified. If the decrease in implied volatility seems
justified, abuyer of volatility should ignore it and look for other opportunities.
All volatility traders should be suspicious when volatility seems to be extreme -
either too expensive or too cheap. The trader should investigate the possibilities as to
why volatility is trading at such extreme levels. In some cases, the supply and demand
of the public just pushes the options to extreme levels; there is nothing more involved
than that. Those are the best volatility trading situations. However, if there is ahint
that the volatility has gotten to an extreme reading because of some logical (but per
haps nonpublic) reason, then the volatility trader should be suspicious and should
probably avoid the trade. Typically this happens with expensive options.
Buyers of volatility really have little to fear if they miscalculate and thus buy an
option that appears inexpensive but turns out not to be, in reality. The volatility buyer
might lose money if he does this, and overpaying for options constantly will lead to
ruin, but an occasional mistake will probably not be fatal.

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748 Part VI: Measuring and Trading Volatility
Sellers of volatility, however, have to be alot more careful. One mistake could
be the last one. Selling naked calls that seem terrifically expensive by historic stan
dards could be ruinous if atakeover bid subsequently emerges at alarge premium to
the stock'scurrent price. Even put sellers must be careful, although alot of traders
think that selling naked puts is safe because it'sthe same as buying stock. But who
ever said buying stock wasn'trisky? If the stock literally collapses - falling from 80,
say, to 15 or 20, as Oxford Health did, or from 30 to 2 as Sunrise Technology did -
then aput seller will be buried. Since the risk of loss from naked option selling is
large, one could be wiped out by ahuge gap opening. That'swhy it'simperative to
study why the options are expensive before one sells them. If it'sknown, for exam
ple, that asmall biotech company is awaiting FDA trial results in two weeks,~and all
the options suddenly become expensive, the volatility seller should not attempt to be
ahero. It'sobvious that at least some traders believe that there is achance for the
stock to gap in price dramatically. It would be better to find some other situation in
which to sell options.
The seller of futures options or index options should be cautious too, although
there can'tbe takeovers in those markets, nor can there be ahuge earnings surprise
or other corporate event that causes abig gap. The futures markets, though do have
things like crop reports and government economic data to deal with, and those can
create volatile situations, too. The bottom line is that volatility selling - even hedged
volatility selling - can be taxing and aggravating if one has sold volatility in front of
what turns out to be anews item that justifies the expensive volatility.
SUMMARY
Volatility trading is apredictable way to approach the market, because volatility
almost invariably trades in arange and therefore its value can be estimated with agreat deal more precision than can the actual prices of the underlyings. Even so, one
must be careful in his approach to volatility trading, because diligent research is
needed to determine if, in fact, volatility is "cheap" or "expensive." As with any sys
tematic approach to the market, if one is sloppy about his research, he cannot expect
to achieve superior results. In the next few chapters, agood deal of time will be spent
to give the reader agood understanding of how volatility affects positions and how it
can be used to construct trades with positive expected rates of return.

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· GHAR:f ER :8'7 . . -
How Volatility Affects
Popular Strategies
The previous chapter addressed the calculation or interpretation of implied volatili
ty, and how to relate it to historic volatility. Another, related topic that is important is
how implied volatility affects aspecific option strategy. Simplistically, one might think
that the effect of achange in implied volatility on an option position would be asim
ple matter to discern; but in reality, most traders don'thave acomplete grasp of the
ways that volatility affects option positions. In some cases, especially option spreads
or more complex positions, one may not have an intuitive "picture" of how his posi
tion is going to be affected by achange in implied volatility. In this chapter, we'll
attempt arelatively thorough review of how implied volatility changes affect most of
the popular option strategies.
There are ways to use computer analysis to "draw" apicture of this volatiiity
effect, of course, and that will be discussed momentarily. But an option strategist
should have some idea of the general changes that aposition will undergo if implied
volatility changes. Before getting into the individual strategies, it is important that
one understands some of the basics of the effect of volatility on an option'sprice.
VEGA
Technically speaking, the term that one uses to quantify the impact of volatility
changes on the price of an option is called the vega of the option. In this chapter, the
references will be to vega, but the emphasis here is on practicality, so the descriptions
749

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750 Part VI: Measuring and Trading Volatility
of how volatility affects option positions will be in plain English as well as in the more
mathematical realm of vega. Having said that, let'sdefine vega so that it is understood
for later use in the chapter.
Simply stated, vega is the amount by which an option'sprice changes when
volatility changes by one percentage point.
Example: XYZ is selling at 50, and the July 50 call is trading at 7.25. Assume that
there is no dividend, that short-term interest rates are 5%, and that July expiration is
exactly three months away. With this information, one can determine that the implied
volatility of the July 50 call is 70%. That'safairly high number, so one can surmise
that XYZ is avolatile stock. What would the option price be if implied volatility were
rise to 71 %? Using amodel, one can determine that the July 50 call would theoreti
cally be worth 7.35 if that happened. Hence, the vega of this option is 0.10 (to two
decimal places). That is, the option price increased by 10 cents, from 7.25 to 7.35,
when volatility rose by one percentage point. (Note that "percentage point" here
means afull point increase in volatility, from 70% to 71 %.)
What if implied volatility had decreased instead? Once again, one can use the
model to determine the change in the option price. In this case, using an implied
volatility of 69% and keeping everything else the same, the option would then theo
retically be worth 7.15- again, a 0.10 change in price (this time, adecrease in price).
This example points out an interesting and important aspect of how volatility
affects acall option: If implied volatility increases, the price of the option will
increase, and if implied volatility decreases, the price of the option will decrease.
Thus, there is adirect relationship between an option'sprice and its implied volatili-
ty.
Mathematically speaking, vega is the partial derivative of the Black-Scholes
model (or whatever model you're using to price options) with respect to volatility. In
the above example, the vega of the July 50 call, with XYZ at 50, can be computed to
be 0.098 - very near the value of 0.10 that one arrived at by inspection.
Vega also has adirect relationship with the price of aput. That is, as implied
volatility rises, the price of aput will rise as well.
Example: Using the same criteria as in the last example, suppose that XYZ is trading
at 50, that July is three months away, that short-term interest rates are 5%, and that
there is no dividend. In that case, the following theoretical put and call prices would
apply at the stated implied volatilities:

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Chapter 37: How Volatility Affects Popular Strategies 751
Stock Price July 50 call July 50 put Implied Volatility Put's Vega
50 7.15 6.54 69% 0.10
7.25 6.64 70% 0.10
7.35 6.74 71% 0.10
Thus, the put'svega is 0.10, too - the same as the call'svega was.
In fact, it can be stated that acall and aput with the same terms have the same
vega. To prove this, one need only refer to the arbitrage equation for aconversion. If
the call increases in price and everything else remains equal - interest rates, stock
price, and striking price - then the put price must increase by the same amount. Achange in implied volatility will cause such achange in the call price, and asimilar
change in the put price. Hence, the vega of the put and the call must be the same.
It is also important to know how the vega changes as other factors change, par
ticularly as the stock price changes, or as time changes. The following examples con
tain several tables that illustrate the behavior of vega in atypically fluctuating envi
ronment.
Example: In this case, let the stock price fluctuate while holding interest rate (5% ),
implied volatility (70%), time (3 months), dividends (0), and the strike price (50) con
stant. See Table 37-1.
In these cases, vega drops when the stock price does, too, but it remains fairly
constant if the stock rises. It is interesting to note, though, that in the real world,
when the underlying drops in price especially if it does so quickly, in apanic mode
- implied volatility can increase dramatically. Such an increase may be of great ben
efit to acall holder, serving to mitigate his losses, perhaps. This concept will be dis
cussed further later in this chapter.
TABLE 37-1
Implied Volatility Theoretical
Stock Price July 50 Call Price Coll Price Vega
30 70% 0.47 0.028
40 2.62 0.073
50 7.25 0.098
60 14.07 0.092
70 22.35 0.091

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752 Part VI: Measuring and Trading Volatility
The above example assumed that the stock was making instantaneous changes
in price. In reality, of course, time would be passing as well, and that affects the vega
too. Table 37-2 shows how the vega changes when time changes, all other factors
being equal.
Example: In this example, the following items are held fixed: stock price (50), strike
price (50), implied volatility (70%), risk-free interest rate (5%), and dividend\(0). But
now, we let time fluctuate.
Table 37-2 clearly shows that the passage of time results not only in adecreas
ing call price, but in adecreasing vega as well. This makes sense, of course, since one
cannot expect an increase in implied volatility to have much of an effect on avery
short-term option - certainly not to the extent that it would affect a LEAPS option.
Some readers might be wondering how changes in implied volatility itself would
affect the vega. This might be called the "vega of the vega," although I've never actu
ally heard it referred to in that manner. The next table explores that concept.
Example: Again, some factors will be kept constant - the stock price (50), the time
to July expiration (3 months), the risk-free interest rate (5%), and the dividend (0).
Table 37-3 allows implied volatility to fluctuate and shows what the theoretical price
of a July 50 call would be, as well as its vega, at those volatilities.
Thus, Table 37-3 shows that vega is surprisingly constant over awide range of
implied volatilities. That'sthe real reason why no one bothers with "vega of the vega."
Vega begins to decline only if implied volatility gets exceedingly high, and implied
volatilities of that magnitude are relatively rare.
One can also compute the distance astock would need to rise in order to over
come adecrease in volatility. Consider Figure 37-1, which shows the theoretical price
TABLE 37-2
Implied Time Theoretical
Stock Price Volatility Remaining Call Price Vega
50 70% One year 14.60 0.182
Six months 10.32 0.135
Three months 7.25 0.098
Two months 5.87 0.080
One month 4.16 0.058
Two weeks 2.87 0.039
One week 1.96 0.028
One day 0.73 0.010

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Chapter 37: How Volatility Affeds Popular Strategies
TABLE 37-3
Implied
Stock Price Volatility
50 10%
30%
50%
70%
100%
150%
200%
Theoretical
Coll Price
1.34
3.31
5.28
7.25
10.16
14.90
19.41
753
Vega
0.097
0.099
0.099
0.098
0.096
0.093
0.088
of a 6-month call option with differing implied volatilities. Suppose one buys an
option that currently has implied volatility of 170% (the top curve on the graph).
Later, investor perceptions of volatility diminish, and the option is trading with an
implied volatility of 140%. That means that the option is now "residing" on the sec
ond curve from the top of the list. Judging from the general distance between those
two curves, the option has probably lost between 5 and 8 points of value due to the
drop in implied volatility.
Here'sanother way to think about it. Again, suppose one buys an at-the-money
option (stock price = 100) when its implied volatility is 170%. That option value is
marked as point Aon the graph in Figure 37-1. Later, the option'simplied volatility
drops to 140%. How much does the stock have to rise in order to overcome the loss
of implied volatility? The horizontal line from point Ato point Bshows that the
option value is the same on each line. Then, dropping avertical line from Bdown to
point C, we see that point Cis at astock price of about 109. Thus, the stock would
have to rise 9 points just to keep the option value constant, if implied volatility drops
from 170% to 140%.
IMPLIED VOLATILITY AND DELTA
Figure 37-1 shows another rather unusual effect: When implied volatility gets very
high, the delta of the option doesn'tchange much. Simplistically, the delta of an
option measures how much the option changes in price when the stock moves one
point. Mathematically, the delta is the first partial derivative of the option model with
respect to stock price. Geometrically, that means that the delta of an option is the
slope of aline drawn tangent to the curve in the preceding chart.

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754 Part VI: Measuring and Trading Volatility
FIGURE 37-1.
Theoretical option prices at differing implied
volatilities (6-month calls).
80
70
Q) 60
(.)
·;:::
Cl.. 50
C:
0
·a 40
0
30
20
10
Stock Price
60 80 100 C 120 140
_JY.._
170%
140%
110%
80%
50%
20%
The bottom line in Figure 37-1 (where implied volatility= 20%) has adistinct
curvature to it when the stock price is between about 80 and 120. Thus the delta
ranges from afairly low number (when the stock is near 80) to arather high number
(when the stock is near 120). Now look at the top line on the chart, where implied
volatility= 170%. It'salmost astraight line from the lower left to the upper right! The
slope of astraight line is constant. This tells us that the delta (which is the slope)
barely changes for such an expensive option - whether the stock is trading at 60 or
it'strading at 150! That fact alone is usually surprising to many.
In addition, the value of this delta can be measured: It's 0. 70 or higher from astock price of 80 all the way up to 150. Among other things, this means that an out~
of-the-money option that has extremely high implied volatility has afairly high delta
- and can be expected to mirror stock price movements more closely than one might
think, were he not privy to the delta.
Figure 37-2 follows through on this concept, showing how the delta of an option
varies with implied volatility. From this chart, it is clear how much the delta of an
option varies when the implied volatility is 20%, as compared to how little it varies
when implied volatility is extremely high.
That data is interesting enough by itself, but it becomes even more thought-pro
voking when one considers that achange in the implied volatility of his option (vega)
also can mean asignificant change in the delta of the option. In one sense, it explains
why, in the first chart (Figure 37-1), the stock could rise 9 points and yet the option
holder made nothing, because implied volatility declined from 170% to 140%.

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Chapter 37: How Volatility Affects Popular Strategies
EFFECTS ON NEUTRALITY
755
Apopular concept that uses delta is the "delta-neutral" spread aspread whose prof
itability is supposedly ambivalent to market movement, at least for short time frames
and limited stock price changes. Anything that significantly affects the delta of an
option can affect this neutrality, thus causing adelta-neutral position to become
unbalanced ( or, more likely, causing one'sintuition to be wrong regarding what con
stitutes adelta-neutral spread in the first place).
Let'suse afamiliar strategy, the straddle purchase, as an example. Simplistically,
when one buys astraddle, he merely buys aput and acall with the same terms and
doesn'tget any fancier than that. However, it may be the case that, due to the deltas
of the options involved, that approach is biased to the upside, and aneutral straddle
position should be established instead.
Example: Suppose that XYZ is trading at 100, that the options have an implied
volatility of 40%, and that one is considering buying asix-month straddle with astrik
ing price of 100. The following data summarize the situation, including the option
prices and the deltas:
XYZ Common: l 00; Implied Volatility: 40%
Option
XYZ October l 00 call
XYZ October l 00 put
FIGURE 37-2.
Price
12.00
10.00
Delta
0.60
-0.40
Value of delta of a 6-month option at differing implied volatilities.
90
80
70
.!!lai 60
Cl
C: 50 ,g
8° 40
30
20
10
60 80 100
Stock Price
120 140

eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:807