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 a strategy might be successful, and to determine whether the
current option price is a relatively cheap one or a relatively expensive one. For exam
ple, one can't just say, "I think XYZ is going to rise at least 18 points by February expi
ration." There needs to be some basis in fact for such a statement 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 a major 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 a particu
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's shortened to GARCH. It is a technique 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 a constant ("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 a
volatility prediction for today (using GARCH, let's say), 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's volatility is likely to be
much like today's. Of course, that's a little bit like saying tomorrow's weather is likely
to be the same as today's (which it is, two-thirds of the time, according to statistics).
It's just that when a tornado 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 a perfect job of estimating and forecasting volatility. In
fact, it might not even be superior, from a strategist's viewpoint, 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 a position 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 a following among theoretically oriented traders and analysts.
MOVING AVERAGES
Some traders try to use moving averages of daily composite implied volatility read
ings, or use a smoothing 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 a
smoothing effect be obtained by taking a moving 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's needed 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 a particular underlying instrument to
produce a single 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's volatility is likely to be
much like today's. Of course, that's a little bit like saying tomorrow's weather is likely
to be the same as today's (which it is, two-thirds of the time, according to statistics).
It's just that when a tornado 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 a perfect job of estimating and forecasting volatility. In
fact, it might not even be superior, from a strategist's viewpoint, 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 a position 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 a following among theoretically oriented traders and analysts.
MOVING AVERAGES
Some traders try to use moving averages of daily composite implied volatility read
ings, or use a smoothing 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 a
smoothing effect be obtained by taking a moving 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's needed 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 a particular underlying instrument to
produce a single 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's volatility is likely to be
much like today's. Of course, that's a little bit like saying tomorrow's weather is likely
to be the same as today's (which it is, two-thirds of the time, according to statistics).
It's just that when a tornado 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 a perfect job of estimating and forecasting volatility. In
fact, it might not even be superior, from a strategist's viewpoint, 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 a position 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 a following among theoretically oriented traders and analysts.
MOVING AVERAGES
Some traders try to use moving averages of daily composite implied volatility read
ings, or use a smoothing 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 a
smoothing effect be obtained by taking a moving 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's needed 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 a particular underlying instrument to
produce a single 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, a trader knows for certain the following items that
affect an option's price: 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's guess 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 a non
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 a company's earnings, 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 a signal that some traders do indeed know the future - at least with respect
to a specific 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 a volatility 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's implied volatility may bear no resemblance to the actual statistical volatility
that later unfolds during the life of the option.
For those who desire a more 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 a particular 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
a way to rank the current implied volatility reading with past readings for the same
underlying instrument.
However, a fairly important ingredient is missing when percentiles are involved.
One can't really tell if "cheap" options are cheap as a practical matter. That's because
one doesn't know 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 a current 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 a
reading of 40% is really quite mundane. There just wouldn't be 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't gain 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 a low 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 a large 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 a practical 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 a cheap 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 a short-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't change 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 a composite 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's difficult 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 a couple of reasons: First, if one
holds the option for any long period of time, the volatility range will widen out and
there is a chance 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 a gain 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's important 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 a good 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 a bit 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 a forward-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 a good predictor of actual volatility?" Somehow, it seems
logical to assume that implied and historical (actual) volatility will converge. That's
not 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's movement speed up or slow down to get in line with implied volatility?
To illustrate this concept, a few 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 a composite 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's implied volatility is weight
ed by trading volume and by distance in- or out-of-the-money, to arrive at a sin
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, a slightly different volatility figure is arrived at, as com
pared to $VIX, but a chart 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 a little 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 a seller 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 a chart similar to Figure 36-4, comparing actual and implied
volatility, and their difference, for a particular 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 a more or less neutral outlook
on the stock. Figure 36-6 shows the stock's performance 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 a month. 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, a major price explosion had begun in the stock, one that tripled its value in
just over a month. Clearly, implied volatility was a poor 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 a few times during the rest of 1999. It
might appear that these oscillations are small and that implied volatility was actually
doing a pretty 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 a circle in Figure 36-8, and the same point
in time is marked with a similar 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 a period 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 a poor 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 a month.
The important thing to note from these figures is that they clearly show that
implied volatility is really not a very 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 a great predictor of
volatility that is to follow, either, especially in the short term. No one really makes any
claims that it is a good predictor, for historical volatility is merely a reflection of what
has happened in the past. All we can say for sure is that implied and historical volatil
ity tend to trade within a range.
One thing that does stand out on these charts is that implied volatility seems to
fluctuate less than actual volatility. That seems to be a natural 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 a rather 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't constitute a rigorous study
upon which to draw the conclusion that implied volatility is a poor predictor of actu
al volatility, but it is this author's firm opinion that that statement is true. A graduate
student looking for a master's thesis topic could take it from here.
VOLATILITY TRADING
As a result 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 a stock is in a relatively
nonvolatile period, like the price of the stock in Figure 36-2, just before point A on
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 a result, 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 a function
of looking at the profit and loss statements in one's option account. But anyone who
took a longer 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 a buyer of
options.
It is the volatility trader's objective to spot situations when implied volatility is
possibly or probably erroneous and to take a position that would profit when the
error is brought to light. Thus, the volatility trader's main 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 a contrarian 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't just 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't just 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 (a takeover or
an earnings surprise, for example).
Since options off er a good deal of leverage, they are an attractive vehicle to any
one who wants to make a quick trade, especially if that person believes he knows
something that the general public doesn't know. Thus, if there is a leak of a takeover
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 a clue to which stocks might be ready to make a big move.
Invariably, if the trading volume has increased and if implied volatility has increased
as well, it is a good warning sign that someone with inside information is buying the
options. In such a case, it might not be a good idea to sell volatility, even though the
options are mathematically expensive.
Sometimes, even more minor news items are known in advance by a small seg
ment of the investing community. If those items will be enough to move the stock
even a couple 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 a high-ranking corporate officer, or perhaps some strategic alliance with another
company, or even a new product announcement.
The seller of volatility can watch for two things as warning signs that perhaps
the options are "predicting" a corporate event (and hence should be avoided as a
"volatility sale"). Those two things are a dramatic increase in option volume or a sud
den jump in implied volatility of the options. One or both can be caused by traders
with inside information trying to obtain a leveraged 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 a large 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't cease 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 a portion of
their institutional stock holdings. Activity of this sort should be a warning 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't have anything to do with insider trad
ing. This might include a large covered call write or maybe a large put purchase
established by an institution as a hedge against an existing stock position, or a rela
tively large conversion or reversal arbitrage established by an arbitrageur, or even a
large spread transaction initiated by a hedge fund. In any of these cases, option vol
ume would jump dramatically, but it wouldn't mean that anyone had inside knowl
edge about a forthcoming 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 a takeover 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 a last 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 a reasonably 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 a
strategy of selling volatility in this case.
However, there is a case 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, a floor 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 a large quantity. If this happens a few times in a row, the options
will have gotten very expensive as the floor broker raises his bid price repeatedly, but
only buys a few 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 a sudden
increase in option volume would not be present. In this case, though, a volatility 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 a short period of time (one day, or actually less time), and that
alone should be enough warning to a volatility 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 a good reason why that is happening. That rea
son will probably become public knowledge shortly in the form of a news event. In
fact, a major 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, a volatility seller should avoid situations such as
these. Any sudden increase in implied volatility should probably be viewed as a
potential news story in the making. These situations are not what a neutral volatility
seller wants to get into.
On the other hand, if options have become expensive as a result of corporate
news, then the volatility seller can feel more comfortable making a trade. Perhaps the
company has announced poor earnings and the stock has taken a beating 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 a few insider traders.
With clear analysis, one might be able to develop a volatility selling strategy that is
prudent and potentially profitable.
Another situation in which options become expensive in the wake of market
action is during a bear 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 a
neutral 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's when insider trading may be present, and that's when 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's stock will be less volatile than the original company's stock was. As the takeover
is in the process of being consummated, the implied volatility of the company's
options will drop, giving the false impression that they are cheap.
In a similar vein, a company 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 a relatively high degree of implied volatility. However, as the com
pany matures, it buys other Internet companies and then perhaps even merges with a
large, 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, a buyer 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, a buyer 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 a hint
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 a lot more careful. One mistake could
be the last one. Selling naked calls that seem terrifically expensive by historic stan
dards could be ruinous if a takeover bid subsequently emerges at a large premium to
the stock's current price. Even put sellers must be careful, although a lot of traders
think that selling naked puts is safe because it's the same as buying stock. But who
ever said buying stock wasn't risky? 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 a put seller will be buried. Since the risk of loss from naked option selling is
large, one could be wiped out by a huge gap opening. That's why it's imperative to
study why the options are expensive before one sells them. If it's known, for exam
ple, that a small 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
a hero. It's obvious that at least some traders believe that there is a chance 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't be takeovers in those markets, nor can there be a huge earnings surprise
or other corporate event that causes a big 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 a news item that justifies the expensive volatility.
SUMMARY
Volatility trading is a predictable way to approach the market, because volatility
almost invariably trades in a range and therefore its value can be estimated with a
great 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, a good deal of time will be spent
to give the reader a good 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 a specific option strategy. Simplistically, one might think
that the effect of a change in implied volatility on an option position would be a sim
ple matter to discern; but in reality, most traders don't have a complete 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 a change in implied volatility. In this chapter, we'll
attempt a relatively thorough review of how implied volatility changes affect most of
the popular option strategies.
There are ways to use computer analysis to "draw" a picture 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 a position 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's price.
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's define vega so that it is understood
for later use in the chapter.
Simply stated, vega is the amount by which an option's price 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's a fairly high number, so one can surmise
that XYZ is a volatile stock. What would the option price be if implied volatility were
rise to 71 %? Using a model, 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 a full 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, a decrease in price).
This example points out an interesting and important aspect of how volatility
affects a call 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 a direct relationship between an option's price 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 a direct relationship with the price of a put. That is, as implied
volatility rises, the price of a put 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's vega is 0.10, too - the same as the call's vega was.
In fact, it can be stated that a call and a put with the same terms have the same
vega. To prove this, one need only refer to the arbitrage equation for a conversion. 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. A
change in implied volatility will cause such a change in the call price, and a similar
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 a typically 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 a panic mode
- implied volatility can increase dramatically. Such an increase may be of great ben
efit to a call 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 a decreas
ing call price, but in a decreasing vega as well. This makes sense, of course, since one
cannot expect an increase in implied volatility to have much of an effect on a very
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 a wide range of
implied volatilities. That's the 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 a stock would need to rise in order to over
come a decrease 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's another 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 A on the graph in Figure 37-1. Later, the option's implied 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 A to point B shows that the
option value is the same on each line. Then, dropping a vertical line from B down to
point C, we see that point C is at a stock 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't change 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 a line 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 a distinct
curvature to it when the stock price is between about 80 and 120. Thus the delta
ranges from a fairly low number (when the stock is near 80) to a rather high number
(when the stock is near 120). Now look at the top line on the chart, where implied
volatility= 170%. It's almost a straight line from the lower left to the upper right! The
slope of a straight 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's trading 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 a
stock 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 a fairly 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 a change in the implied volatility of his option (vega)
also can mean a significant 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
A popular concept that uses delta is the "delta-neutral" spread a spread 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 a delta-neutral position to become
unbalanced ( or, more likely, causing one's intuition to be wrong regarding what con
stitutes a delta-neutral spread in the first place).
Let's use a familiar strategy, the straddle purchase, as an example. Simplistically,
when one buys a straddle, he merely buys a put and a call with the same terms and
doesn't get 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 a neutral 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 a six-month straddle with a strik
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
.!!l
ai 60
Cl
C: 50 ,g
8° 40
30
20
10
60 80 100
Stock Price
120 140

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756 Part VI: Measuring and Trading Volatility
Notice that the stock price is equal to the strike price (100). However, the deltas
are not at all equal. In fact, the delta of the call is 1.5 times that of the put (in absolute
value). One must buy three puts and two calls in order to have a delta-neutral posi
tion.
Most experienced option traders know that the delta of an at-the-money call is
somewhat higher than that of an at-the-money put. Consequently, they often esti
mate, without checking, that buying three puts and two calls produces a delta-neu
tral "straddle buy." However, consider a similar situation, but with a much higher
implied volatility- 110%, say.
AAA Common: 100; Implied Volatility: 110%
Option
AAA October 100 call
AAA October 1 00 put
Price
31.00
28.00
Delta
0.67
-0.33
The delta-neutral ratio here is two-to-one (67 divided by 33), not three-to-two
as in the earlier case - even though both stock prices are 100 and both sets of options
have six months remaining. This is a big difference in the delta-neutral ratio, espe
cially if one is trading a large quantity of options. This shows how different levels of
implied volatility can alter one's perception of what is a neutral position. It also points
out that one can't necessarily rely on his intuition; it is always best to check with a
model.
Carrying this thought a step further, one must be mindful of a change in implied
volatility if he wants to keep his position delta-neutral. If the implied volatility of AAA
options should drop significantly, the 2-to-l ratio will no longer be neutral, even if the
stock is still trading at 100. Hence, a trader wishing to remain delta-neutral must
monitor not only changes in stock price, but changes in implied volatility as well. For
more complex strategies, one will also find the delta-neutral ratio changing due to a
change in implied volatility.
The preceding examples summarize the major variables that might affect the
vega and also show how vega affects things other than itself, such as delta and, there
fore, delta neutrality. By the way, the vega of the underlying is zero; an increase in
implied volatility does not affect the price of the underlying instrument at all, in the
ory. In reality, if options get very expensive (i.e., implied volatility spikes up), that
usually brings traders into a stock and so the stock price will change. But that's not a
mathematical relationship, just a market cause-and-effect relationship.

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Chapter 37: How Volatility Affects Popular Strategies
POSITION VEGA
757
As can be done with delta or with any other of the partial derivatives of the model,
one can compute a position vega - the vega of an entire position. The position vega
is determined by multiplying the individual option vegas by the quantity of options
bought or sold. The "position vega" is merely the quantity of options held, times the
vega, times the shares per options ( which is normally 100).
Example: Using a simple call spread as an example, assume the following prices
exist:
Security Position Vega Position Vego
XYZ Stock No position
XYZ July 50 call Long 3 calls 0.098 +0.294
XYZ July 70 call Short 5 calls 0.076 -0.380
Net Position Vega: -0.086
This concept is very important to a volatility trader, for it tells him if he has con
structed a position that is going to behave in the manner he expects. For example,
suppose that one identifies expensive options, and he figures that implied volatility
will decrease, eventually becoming more in line with its historical norms. Then he
would want to construct a position with a negative position vega. A negative position
vega indicates that the position will profit if implied volatility decreases. Conversely,
a buyer of volatility - one who identifies some underpriced situation - would want to
construct a position with a positive position vega, for such a position will profit if
implied volatility rises. In either case, other factors such as delta, time to expiration,
and so forth will have an effect on the position's actual dollar profit, but the concept
of position vega is still important to a volatility trader. It does no good to identify
cheap options, for example, and then establish some strange spread with a negative
position vega. Such a construct would be at odds with one's intended purpose - in
this case, buying cheap options.
OUTRIGHT OPTION PURCHASES AND SALES
Let us now begin to investigate the affects of implied volatility on various strategies,
beginning with the simplest strategy of all - the outright option purchase. It was
already shown that implied volatility affects the price of an individual call or put in a

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758 Part VI: Measuring and Trading Volatility
direct manner. That is, an increase in implied volatility will cause the option price to
rise, while a decrease in volatility will cause a decline in the option price. That piece
of information is the most important one of all, for it imparts what an option trader
needs to know: An explosion in implied volatility is a boon to an option owner, but
can be a devastating detriment to an option seller, especially a naked option seller.
A couple of examples might demonstrate more clearly just how powerful the
effect of implied volatility is, even when there isn't much time remaining in the life
of an option. One should understand the notion that an increase in implied volatility
can overcome days, even weeks, of time decay. This first example attempts to quan
tify that statement somewhat.
Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3-
month call with striking price of 100. Furthermore, suppose that implied volatility is
currently at 20%. Given these assumptions, the Black-Scholes model tells us that the
call would be trading at a price of 4.64.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
20%
4.64
Now, suppose that a month passes. If implied volatility remained the same
(20% ), the call would lose nearly a point of value due to time decay. However, how
much would implied volatility have had to increase to completely counteract the
effect of that time decay? That is, after a month has passed, what implied volatility
will yield a call price of 4.64? lt turns out to be just under 26%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
25.9%
4.64
What would happen after another month passes? There is, of course, some
implied volatility at which the call would still be worth 4.64, but is it so high as to be
unreasonable? Actually, it turns out that if implied volatility increases to about 38%,
the call will still be worth 4.64, even with only one month of life remaining:

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Chapter 37: How Volatility Affects Popular Strategies
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
1 month
38.1%
4.64
759
So, if implied volatility increases from 20% to 26% over the first month, then
this call option would still be trading at the same price - 4.64. That's not an unusual
increase in implied volatility; increases of that magnitude, 20% to 26%, happen all
the time. For it to then increase from 26% to 38% over the next month is probably
less likely, but it is certainly not out of the question. There have been many times in
the past when just such an increase has been possible - during any of the August,
September, or October bear markets or mini-crashes, for example. Also, such an
increase in implied volatility might occur if there were takeover rumors in this stock,
or if the entire market became more volatile, as was the case in the latter half of the
1990s.
Perhaps this example was distorted by the fact that an implied volatility of 20%
is a fairly low number to begin with. What would a similar example look like if one
started out with a much higher implied volatility - say, 80%?
Example: Making the same assumptions as in the previous example, but now setting
the implied volatility to a much higher level of 80%, the Black-Scholes model now
says that the call would be worth a price of 16.45:
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
80%
16.45
Again, one must ask the question: "If a month passes, what implied volatility
would be necessary for the Black-Scholes model to yield a price of 16.45?" In this
case, it turns out to be an implied volatility of just over 99%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
99.4%
16.45

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758 Part VI: Measuring and Trading Volatility
direct manner. That is, an increase in implied volatility will cause the option price to
rise, while a decrease in volatility will cause a decline in the option price. That piece
of information is the most important one of all, for it imparts what an option trader
needs to know: An explosion in implied volatility is a boon to an option owner, but
can be a devastating detriment to an option seller, especially a naked option seller.
A couple of examples might demonstrate more clearly just how powerful the
effect of implied volatility is, even when there isn't much time remaining in the life
of an option. One should understand the notion that an increase in implied volatility
can overcome days, even weeks, of time decay. This first example attempts to quan
tify that statement somewhat.
Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3-
month call with striking price of 100. Furthermore, suppose that implied volatility is
currently at 20%. Given these assumptions, the Black-Scholes model tells us that the
call would be trading at a price of 4.64.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
20%
4.64
Now, suppose that a month passes. If implied volatility remained the same
(20% ), the call would lose nearly a point of value due to time decay. However, how
much would implied volatility have had to increase to completely counteract the
effect of that time decay? That is, after a month has passed, what implied volatility
will yield a call price of 4.64? It turns out to be just under 26%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
25.9%
4.64
What would happen after another month passes? There is, of course, some
implied volatility at which the call would still be worth 4.64, but is it so high as to be
unreasonable? Actually, it turns out that if implied volatility increases to about 38%,
the call will still be worth 4.64, even with only one month of life remaining:

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Chapter 37: How Volatility Affects Popular Strategies
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
1 month
38.1%
4.64
759
So, if implied volatility increases from 20% to 26% over the first month, then
this call option would still be trading at the same price 4.64. That's not an unusual
increase in implied volatility; increases of that magnitude, 20% to 26%, happen all
the time. For it to then increase from 26% to 38% over the next month is probably
less likely, but it is certainly not out of the question. There have been many times in
the past when just such an increase has been possible - during any of the August,
September, or October bear markets or mini-crashes, for example. Also, such an
increase in implied volatility might occur if there were takeover rumors in this stock,
or if the entire market became more volatile, as was the case in the latter half of the
1990s.
Perhaps this example was distorted by the fact that an implied volatility of 20%
is a fairly low number to begin with. What would a similar example look like if one
started out with a much higher implied volatility say, 80%?
Example: Making the same assumptions as in the previous example, but now setting
the implied volatility to a much higher level of 80%, the Black-Scholes model now
says that the call would be worth a price of 16.45:
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
80%
16.45
Again, one must ask the question: "If a month passes, what implied volatility
would be necessary for the Black-Scholes model to yield a price of 16.45?" In this
case, it turns out to be an implied volatility of just over 99%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
99.4%
16.45

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760 Part VI: Measuring and Trading Volatility
Finally, to be able to completely compare this example with the previous one, it
is necessary to see what implied volatility would have to rise to in order to offset the
effect of yet another month's time decay. It turns out to be over 140%:
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
1 month
140.9%
16.45
Table 37-4 summarizes the results of these examples, showing the levels to
which implied volatility would have to rise to maintain the call's value as time passes.
Are the volatility increases in the latter example less likely to occur than the
ones in the former example? Probably yes - certainly the last one, in which implied
volatility would have to increase from 80% to nearly 141 % in order to maintain the
call's value. However, in another sense, it may seem more reasonable: Note that the
increase in volatility from 20% to 26% is a 30% increase. That is, 20% times 1.30
equals 26%. That's what's required to maintain the call's value for the lower volatility
over the first month - an increase in the magnitude of implied volatility of 30%. At
the higher volatility, though, an increase in magnitude of only about 25% is required
(from 80% to 99%). Thus, in those terms, the two appear on more equal footing.
What makes the top line of Table 37-4 appear more likely than the bottom line
is merely the fact that an experienced option trader knows that many stocks have
implied volatilities that can fluctuate in the 20% to 40% range quite easily. However,
there are far fewer stocks that have implied volatilities in the higher range. In fact,
until the Internet stocks got hot in the latter portion of the 1990s, the only ones with
volatilities like those were very low-priced, extremely volatile stocks. Hence one's
experience factor is lower with such high implied volatility stocks, but it doesn't mean
that the volatility fluctuations appearing in Table 37-4 are impossible.
If the reader has access to a software program containing the Black-Scholes
model, he can experiment with other situations to see how powerful the effect of
implied volatility is. For example, without going into as much detail, if one takes the
case of a 12-month option whose initial implied volatility is 20%, all it takes to main-
TABLE 37-4
Initial Implied
Volatility
20%
80%
Volatility Leveled Required to Maintain Call Value ...
... After One Month ... After Two Months
26%
99%
38%
141%

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Chapter 37: How Volatility Affects Popular Strategies 761
tain the call's value over a 6-month time period is an increase in implied volatility to
27%. Taken from the viewpoint of the option seller, this is perhaps most enlighten
ing: If you sell a one-year (LEAPS) option and six months pass, during which time
implied volatility increases from 20% to 27% - certainly quite possible -you will have
made nothing! The call will still be selling for the same price, assuming the stock is
still selling for the same price.
Finally, it was mentioned earlier that implied volatility often explodes during a
market crash. In fact, one could determine just how much of an increase in implied
volatility would be necessary in a market crash in order to maintain the call's value.
This is similar to the first example in this section, but now the stock price will be
allowed to decrease as well. Table 37-5, then, shows what implied volatility would be
required to maintain the call's initial value (a price of 4.64), when the stock price falls.
The other factors remain the same: time remaining (3 months), striking price (100),
and interest rate (5% ). Again, this table shows instantaneous price changes. In real
life, a slightly higher implied volatility would be necessary, because each market crash
could take a day or two.
Thus, from Table 37-5, one could say that even if the underlying stock dropped
20 points (which is 20% in this case) in one day, yet implied volatility exploded from
20% to 67% at the same time, the call's value would be unchanged! Could such an
outrageous thing happen? It has: In the Crash of '87, the market plummeted 22% in
one day, while the Volatility Index ($VIX) theoretically rose from 36% to 150% in one
day. In fact, call buyers of some $OEX options actually broke even or made a little
money due to the explosion in implied volatility, despite the fact that the worst mar
ket crash in history had occurred.
If nothing else, these examples should impart to the reader how important it is
to be aware of implied volatility at the time an option position is established. If you
are buying options, and you buy them when implied volatility is "low," you stand to
TABLE 37-5
Stock Price
100
95
90
85
80
75
70
Implied Volatility Necessary for Call to Maintain Value
20% (the initial parameters)
33%
44%
55%
67%
78%
89%

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762 Part VI: Measuring and Trading Volatility
benefit if implied volatility merely returns to "normal" levels while you hold the posi
tion. Of course, having the underlying increase in price is also important.
Conversely, an option seller should be keenly aware of implied volatility when
the option is initially sold - perhaps even more so than the buyer of an option. This
pertains equally well to naked option writers and to covered option writers. If implied
volatility is "too low" when the option writing position is established, then an increase
(or worse, an explosion) in implied volatility will be very detrimental to the position,
completely overcoming the effects of time decay. Hence, an option writer should not
just sell options because he thinks he is collecting time decay each day that passes.
That may be true, but an increase in implied volatility can completely domin.ate what
little time decay might exist, especially for a longer-term option.
In a similar manner, a decrease in implied volatility can be just as important.
Thus, if the call buyer purchases options that are "too costly," ones in which implied
volatility is "too high," then he could lose money even if the underlying makes a mod
est move in his favor.
In the next chapters, the topic of just how an option buyer or seller should
measure implied volatility to determine what is "too low" or "too high" will be dis
cussed. For now, suffice it to grasp the general concept that a change in implied
volatility can have substantial effects on an option's price far greater effects than the
passage of time can have.
In fact, all of this calls into question just exactly what time value premium is.
That part of an option's value that is not intrinsic value is really affected much more
by volatility than it is by time decay, yet it carries the term "time value premium."
TIME VALUE PREMIUM IS A MISNOMER
Many (perhaps novice) option traders seem to think of time as the main antagonist to
an option buyer. However, when one really thinks about it, he should realize that the
portion of an option that is not intrinsic value is really much more related to stock
price movement and/or volatility than anything else, at least in the short term. For
this reason, it might be beneficial to more closely analyze just what the "excess value"
portion of an option represents and why a buyer should not primarily think of it as
time value premium.
An option's price is composed of two parts: (1) intrinsic value, which is the "real"
part of the option's value - the distance by which the option is in-the-money, and (2)
"excess value" - often called time value premium. There are actually five factors that
affect the "excess value" portion of an option. Eventually, time will dominate them

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Chapter 37: How Volah'lity Affects Popular Strategies 763
all, but the longer the life of the option, the more the other factors influence the
"excess value."
The five factors influencing excess value are:
1. stock price movements,
2. changes in implied volatility,
3. the passage of time,
4. changes in the dividend (if any exist), and
5. changes in interest rates.
Each is stated in terms of a movement or change; that is, these are not static
things. In fact, to measure them one uses the "greeks": delta, vega, theta, (there is no
"greek" for dividend change), and rho. Typically, the effect of a change in dividend or
a change in interest rate is small (although a large dividend change or an interest rate
change on a very long-term option can produce visible changes in the prices of
options).
If everything remains static, then time decay will eventually wipe out all of the
excess value of an option. That's why it's called time value premium. But things don't
ever remain static, and on a daily basis, time decay is small, so it is the remaining two
factors that are most important.
Example: XYZ is trading at 82 in late November. The January 80 call is trading at 8.
Thus, the intrinsic value is 2 (82 minus 80) and the excess value is 6 (8 minus 2). If
the stock is still at 82 at January expiration, the option will of course only be worth 2,
and one will say that the 6 points of excess value that was lost was due to time decay.
But on that day in late November, the other factors are much more dominant.
On this particular day, the implied volatility of this option is just over 50%. One
can determine that the call's greeks are:
Delta: 0.60
Vega: 0.13
Theta: -0.06
This means, for example, that time decay is only 6 cents per day. It would
increase as time went by, but even with a day or so to go, theta would not increase
above about 20 cents unless volatility increased or the stock moved closer to the
strike price.
From the above figures, one can see - and this should be intuitively appealing that
the biggest factor influencing the price of the option is stock price movement (delta).

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764 Part VI: Measuring and Trading VolatiRty
It's a little unfair to say that, because it's conceivable (although unlikely) that volatil
ity could jump by a large enough margin to become a greater factor than delta for
one day's move in the option. Furthermore, since this option is composed mostly of
excess value, these more dominant forces influence the excess value more than time
decay does.
There is a direct relationship between vega and excess value. That is, if implied
volatility increases, the excess value portion of the option will increase and, if implied
volatility decreases, so will excess value.
The relationship between delta and excess value is not so straightforward. The
farther the stock moves away from the strike, the more this will have the effect of
shrinking the excess value. If the call is in-the-money (as in the above example), then
an increase in stock price will result in a decrease of excess value. That is, a deeply in
the-money option is composed primarily of intrinsic value, while excess value is quite
small. However, when the call is out-of-the-money, the effect is just the opposite:
Then, an increase in call price will result in an increase in excess value, because the
stock price increase is bringing the stock closer to the option's striking price.
For some readers, the following may help to conceptualize this concept. The
part of the delta that addresses excess value is this:
Out-of-the-money call: 100% of the delta affects the excess value.
In-the-money call: "1.00 minus delta" affects the excess value. (So, if a call is very
deeply in-the-money and has a delta of 0.95, then the delta only has 1.00 - 0.95,
or 0.05, room to increase. Hence it has little effect on what small amount of
excess value remains in this deeply in-the-money call.)
These relationships are not static, of course. Suppose, for example, that in the
same situation of the stock trading at 82 and the January 80 call trading at 8, there is
only week remaining until expiration! Then the implied volatility would be 155%
(high, but not unheard of in volatile times). The greeks would bear a significantly dif
ferent relationship to each other in this case, though:
Delta: 0.59
Vega: 0.044
Theta: -0 .5 1
This very short-term option has about the same delta as its counterpart in the previ
ous example (the delta of an at-the-money option is generally slightly above 0.50).
Meanwhile, vega has shrunk. The effect of a change in volatility on such a short-term
option is actually about a third of what it was in the previous example. However, time
decay in this example is huge, amounting to half a point per day in this option.

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Chapter 37: How Volatility Affects Popular Strategies 765
So now one has the idea of how the excess value is affected by the "big three"
of stock price movement, change in implied volatility, and passage of time. How can
one use this to his advantage? First of all, one can see that an option's excess value
may be due much more to the potential volatility of the underlying stock, and there
fore to the option's implied volatility, than to time.
As a result of the above information regarding excess value, one shouldn't think
that he can easily go around selling what appear to be options with a lot of excess
value and then expect time to bring in the profits for him. In fact, there may be a lot
of volatility both actual and implied - keeping that excess value nearly intact for a
fairly long period of time. In fact, in the coming chapters on volatility estimation, it
will be shown that option buyers have a much better chance of success than conven
tional wisdom has maintained.
VOLATILITY AND THE PUT OPTION
While it is obvious that an increase in implied volatility ½ill increase the price of a put
option, much as was shown for a call option in. the preceding discussion, there are
certain differences between a put and a call, so a little review of the put option itself
may be useful. A put option tends to lose its premium fairly quickly as it becomes an
in-the-money option. This is due to the realities of conversion arbitrage. In a con
version arbitrage, an arbitrageur or market-maker buys stock and buys the put, while
selling the call. If he carries the position to expiration, he will have to pay carrying
costs on the debit incurred to establish the position. Furthermore, he would earn any
dividends that might be paid while he holds the position. This information was pre
sented in a slightly different form in the chapter on arbitrage, but it is recounted
here:
In a perfect world, all option prices would be so accurate that there would be
no profit available from a conversion. That is, the following equation (1) would apply:
(1) Call price+ Strike price - Stock price - Put price+ Dividend- Carrying cost= 0
where carrying cost = strike price/ (1 + r)t
t = time to expiration
r = interest rate
Now, it is also known that the time value premium of a put is the amount by which
its value exceeds intrinsic value. The intrinsic value of an in-the-money put option is
merely the difference between the strike price and the stock price. Hence, one can
write the following equation (2) for the time value premium (TVP) of an in-the
money put option:

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