IV is acommon cause of time-spread failure for market makers. When iin the front month rises, the volatility of the back-months sometimes does
as well. When this happens, it’soften because market makers who sold
front-month options to retail or institutional buyers buy the back-month
options to hedge their short-gamma risk. If the market maker buys enough
back-month options, he or she will accumulate positive vega. But when the
market sells the front-month volatility back to the market makers, the back
months drop, too, because market makers no longer need the back months
for ahedge.
Traders should study historical implied volatility to avoid this pitfall. As
is always the case with long vega strategies, there is arisk of adecline in
IV. Buying long-term options with implied volatility in the lower third of
the 12-month IV range helps improve the chances of success, since the
volatility being bought is historically cheap.
This can be tricky, however. If atrader looks back on achart of IV for an
option class and sees that over the past six months it has ranged between 20
and 30 but nine months ago it spiked up to, say, 55, there must be areason.
This solitary spike could be just an anomaly. To eliminate the noise from
volatility charts, it helps to filter the data. News stories from that time
period and historical stock charts will usually tell the story of why volatility
spiked. Often, it is aone-time event that led to the spike. Is it reasonable to
include this unique situation when trying to get afeel for the typical range
of implied volatility? Usually not. This is ajudgment call that needs to be
made on acase-by-case basis. The ultimate objective of this exercise is to
determine: “Is volatility cheap or expensive?”

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Buying the Front, Selling the Back
All trading is based on the principle of “buy low, sell high”—even volatility
trading. With time spreads, we can do both at once, but we are not limited
to selling the front and buying the back. When short-term options are
trading at alower IV than long-term ones, there may be an opportunity to
sell the calendar. If the IV of the front month is 17 and the back-month IV is
25, for example, it could be awise trade to buy the front and sell the back.
But selling time spreads in this manner comes with its own unique set of
risks.
First, ashort calendar’sgreeks are the opposite of those of along
calendar. This trade has negative theta with positive gamma. Asideways
market hurts this position as negative theta does its damage. Each day of
carrying the position is paid for with time decay.
The short calendar is also ashort-vega trade. At face value, this implies
that adrop in IV leads to profit and that the higher the IV sold in the back
month, the better. As with buying acalendar, there are some caveats to this
logic.
If there is an across-the-board decline in IV, the net short vega will lead to
aprofit. But an across-the-board drop in volatility, in this case, is probably
not arealistic expectation. The front month tends to be more sensitive to
volatility. It is acommon occurrence for the front month to be “cheap”
while the back month is “expensive.”
The volatilities of the different months can move independently, as they
can when one buys atime spread. There are acouple of scenarios that might
lead to the back-month volatility’sbeing higher than the front month. One is
high complacency in the short term. When the market collectively sells
options in expectation of lackluster trading, it generally prefers to sell the
short-term options. Why? Higher theta. Because the trade has less time until
expiration, the trade has ashorter period of risk. Because of this, selling
pressure can push down IV in the front-month options more than in the
back. Again, the front month is more sensitive to changes in implied
volatility.

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Because volatility has peaks and troughs, this can be asmart time to sell acalendar. The focus here is in seeing the “cheap” front month rise back up
to normal levels, not so much in seeing the “expensive” back month fall.
This trade is certainly not without risk. If the market doesn’tmove, the
negative theta of the short calendar leads to aslow, painful death for
calendar sellers.
Another scenario in which the back-month volatility can trade higher than
the front is when the market expects higher movement after the expiration
of the short-term option but before the expiration of the long-term option.
Situations such as the expectation of the resolution of alawsuit, aproduct
announcement, or some other one-time event down the road are
opportunities for the market to expect such movement. This strategy
focuses on the back-month vol coming back down to normal levels, not on
the front-month vol rising. This can be amore speculative situation for avolatility trade, and more can go wrong.
The biggest volatility risk in selling atime spread is that what goes up can
continue to go up. The volatility disparity here is created by hedgers and
speculators favoring long-term options, hence pushing up the volatility, in
anticipation of abig future stock move. As the likely date of the anticipated
event draws near, more buyers can be attracted to the market, driving up IV
even further. Realized volatility can remain low as investors and traders lie
in wait. This scenario is doubly dangerous when volatility rises and the
stock doesn’tmove. Atrader can lose on negative theta and lose on negative
vega.

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A Directional Approach
Calendar spreads are often purchased when the outlook for the underlying is
neutral. Sell the short-term ATM option; buy the long-term ATM option;
collect theta. But with negative gamma, these trades are never really
neutral. The delta is constantly changing, becoming more positive or
negative. It’slike arubber band: at times being stretched in either direction
but always demanding apull back to the strike. When the strike price being
traded is not ATM, calendar spreads can be strategically traded as
directional plays.
Buying acalendar, whether using calls or puts, where the strike price is
above the current stock price is abullish strategy. With calls, the positive
delta of the long-term out-of-the-money (OTM) call will be greater than the
negative delta of the short-term OTM call. For puts, the positive delta of the
short-term in-the-money (ITM) put will be greater than the negative delta of
the long-term ITM put.
Just the opposite applies if the strike price is below the current stock
price. The negative delta of the short-term ITM call is greater than the
positive delta of the long-term ITM call. The negative delta of the long-term
OTM put is greater than the positive delta of the short-term OTM put.
When the position starts out with either apositive or negative delta,
movement in the direction of the delta is necessary for the trade to be
profitable. Negative gamma is also an important strategic consideration.
Stock-price movement is needed, but not too much.
Buying calendar spreads is like playing outfield in abaseball game. To
catch afly ball, an outfielder must focus on both distance and timing. He
must gauge how far the ball will be hit and how long it will take to get
there. With calendars, the distance is the strike price—that’swhere the stock
needs to be—and the time is the expiration day of the short month’soption:
that’swhen it needs to be at the target price.
For example, with Wal-Mart (WMT) at $48.50, atrader, Pete, is looking
for arise to about $50 over the next five or six weeks. Pete buys the
August–September call calendar. In this example, August has 39 days until
expiration and September has 74 days.

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Exactly what does 50 cents buy Pete? The stock price sitting below the
strike price means anet positive delta. This long time spread also has
positive theta and vega. Gamma is negative. Exhibit 11.8 shows the
specifics.
EXHIBIT 11.8 10-lot Wal-Mart August–September 50 call calendar.
The delta of this trade, while positive, is relatively small with 39 days left
until August expiration. It’snot rational to expect aquick profit if the stock
advances faster than expected. But ultimately, arise in stock price is the
goal. In this example, Wal-Mart needs to rise to $50, and timing is
everything. It needs to be at that price in 39 days. In the interim, amove too
big and too fast in either direction hurts the trade because of negative
gamma. Starting with Wal-Mart at $48.50, delta/gamma problems are worse
to the downside. Exhibit 11.9 shows the effects of stock price on delta,
gamma, and theta.
EXHIBIT 11.9 Stock price movement and greeks.

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The In-or-Out Crowd
Pete could just as well have traded the Aug–Sep 50 put calendar in this
situation. If he’dbeen bearish, he could have traded either the Aug–Sep 45
call spread or the Aug–Sep 45 put spread. Whether bullish or bearish, as
mentioned earlier, the call calendar and the put calendar both function about
the same. When deciding which to use, the important consideration is that
one of them will be in-the-money and the other will be OTM. Whether you
have an ITM spread or an OTM spread has potential implications for the
success of the trade.
The bid-ask spreads tend to be wider for higher-delta, ITM options.
Because of this, it can be more expensive to enter into an ITM calendar.
Why? Trading options with wider markets requires conceding more edge.
Take the following options series:
By buying the May 50 calls at 3.20, atrader gives up 0.10 of theoretical
edge (3.20 is 0.10 higher than the theoretical value). Buying the put at 1.00
means buying only 0.05 over theoretical.
Because acalendar is atwo-legged spread, the double edge given up by
trading the wider markets of two in-the-money options can make the out-of-
the-money spread amore attractive trade. The issue of wider markets is
compounded when rolling the spread. Giving up anickel or adime each
month can add up, especially on nominally low-priced spreads. It can cut
into ahigh percentage of profits.
Early assignment can complicate ITM calendars made up of American
options, as dividends and interest can come into play. The short leg of the
spread could get assigned before the expiration date as traders exercise calls
to capture the dividend. Short ITM puts may get assigned early because of
interest.
Although assignment is an undesirable outcome for most calendar spread
traders, getting assigned on the short leg of the calendar spread may not
necessarily create asignificantly different trade. If along put calendar, for

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Double Calendars
Definition : Adouble calendar spread is the execution of two calendar
spreads that have the same months in common but have two different strike
prices.
Example
Sell 1 XYZ February 70 call
Buy 1 XYZ March 70 call
Sell 1 XYZ February 75 call
Buy 1 XYZ March 75 call
Double calendars can be traded for many reasons. They can be vega
plays. If there is avolatility-time skew, adouble calendar is away to take aposition without concentrating delta or gamma/theta risk at asingle strike.
This spread can also be agamma/theta play. In that case, there are two
strikes, so there are two potential focal points to gravitate to (in the case of
along double calendar) or avoid (in the case of ashort double calendar).
Selling the two back-month strikes and buying the front-month strikes
leads to negative theta and positive gamma. The positive gamma creates
favorable deltas when the underlying moves. Positive or negative deltas can
be covered by trading the underlying stock. With positive gamma, profits
can be racked up by buying the underlying to cover short deltas and
subsequently selling the underlying to cover long deltas.
Buying the two back-month strikes and selling the front-month strikes
creates negative gamma and positive theta, just as in aconventional
calendar. But the underlying stock has two target price points to shoot for at
expiration to achieve the maximum payout.
Often double calendars are traded as IV plays. Many times when they are
traded as IV plays, traders trade the lower-strike spread as aput calendar
and the higher-strike spread acall calendar. In that case, the spread is
sometimes referred to as astrangle swap . Strangles are discussed in
Chapter 15.

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Two Courses of Action
Although there may be many motivations for trading adouble calendar,
there are only two courses of action: buy it or sell it. While, for example,
the trader’sgoal may be to capture theta, buying adouble calendar comes
with the baggage of the other greeks. Fully understanding the
interrelationship of the greeks is essential to success. Option traders must
take aholistic view of their positions.
Let’slook at an example of buying adouble calendar. In this example,
Minnesota Mining & Manufacturing (MMM) has been trading in arange
between about $85 and $97 per share. The current price of Minnesota
Mining & Manufacturing is $87.90. Economic data indicate no specific
reasons to anticipate that Minnesota Mining & Manufacturing will deviate
from its recent range over the next month—that is, there is nothing in the
news, no earnings anticipated, and the overall market is stable. August IV is
higher than October IV by one volatility point, and October implied
volatility is in line with 30-day historical volatility. There are 38 days until
August expiration, and 101 days until October expiration.
The Aug–Oct 85–90 double calendar can be traded at the following
prices:
Much like atraditional calendar spread, the price points cannot be
definitively plotted on a P&(L) diagram. What is known for certain is that at
August expiration, the maximum loss is $3,200. While it’scomforting to
know that there is limited loss, losing the entire premium that was paid for
the spread is an outcome most traders would like to avoid. We also know
the maximum gains occur at the strike prices; but not exactly what the
maximum profit can be. Exhibit 11.10 provides an alternative picture of the
position that is useful in managing the trade on aday-to-day basis.

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EXHIBIT 11.10 10-lot Minnesota Mining & Manufacturing Aug–Oct 85–
90 double call calendar.
These numbers are agood representation of the position’srisk. Knowing
that long calendars and long double calendars have maximum losses at the
expiration of the short-term option equal to the net premiums paid, the max
loss in this example is 3.20. Break-even prices are not relevant to this
position because they cannot be determined with any certainty. What is
important is to get afeel for how much movement can hurt the position.
To make $19 aday in theta, a −0.468 gamma must be accepted. In the
long run, $1 of movement is irrelevant. In fact, some movement is favorable
because the ideal point for MMM to be at, at August expiration is either $85
or $90. So while small moves are acceptable, big moves are of concern. The
negative gamma is an illustration of this warning.
The other risk besides direction is vega. Apositive 1.471 vega means the
calendar makes or loses about $147 with each one-point across-the-board
change in implied volatility. Implied volatility is arisk in all calendar
trades. Volatility was one of the criteria studied when considering this trade.
Recall that the August IV was one point higher than the October and that
the October IV was in line with the 30-day historical volatility at inception
of the trade.
Considering the volatility data is part of the due diligence when
considering acalendar or adouble calendar. First, the (slightly) more
expensive options (August) are being sold, and the cheaper ones are being
bought (October). Astudy of the company reveals no news to lead one to
believe that Minnesota Mining & Manufacturing should move at ahigher
realized volatility than it currently is in this example. Therefore, the front

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Diagonals
Definition : Adiagonal spread is an option strategy that involves buying one
option and selling another option with adifferent strike price and with adifferent expiration date. Diagonals are another strategy in the time spread
family.
Diagonals enable atrader to exploit opportunities similar to those
exploited by acalendar spread, but because the options in adiagonal spread
have two different strike prices, the trade is more focused on delta. The
name diagonal comes from the fact that the spread is acombination of ahorizontal spread (two different months) and avertical spread (two different
strikes).
Say it’s 22 days until January expiration and 50 days until February
expiration. Apple Inc. (AAPL) is trading at $405.10. Apple has been in an
uptrend heading toward the peak of its six-month range, which is around
$420. Atrader, John, believes that it will continue to rise and hit $420 again
by February expiration. Historical volatility is 28 percent. The February 400
calls are offered at a 32 implied volatility and the January 420 calls are bid
on a 29 implied volatility. John executes the following diagonal:
Exhibit 11.11 shows the analytics for this trade.
EXHIBIT 11.11 Apple January–February 400–420 call diagonal.

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From the presented data, is this agood trade? The answer to this question
is contingent on whether the position John is taking is congruent with his
view of direction and volatility and what the market tells him about these
elements.
John is bullish up to August expiration, and the stock in this example is in
an uptrend. Any rationale for bullishness may come from technical or
fundamental analysis, but techniques for picking direction, for the most
part, are beyond the scope of this book. Buying the lower strike in the
February option gives this trade amore positive delta than astraight
calendar spread would have. The trader’sdelta is 0.255, or the equivalent of
about 25.5 shares of Apple. This reflects the trader’sdirectional view.
The volatility is not as easy to decipher. Aspecific volatility forecast was
not stated above, but there are afew relevant bits of information that should
be considered, whether or not the trader has aspecific view on future
volatility. First, the historical volatility is 28 percent. That’slower than
either the January or the February calls. That’snot ideal. In aperfect world,
it’sbetter to buy below historical and sell above. To that point, the February
option that John is buying has ahigher volatility than the January he is
selling. Not so good either. Are these volatility observations deal breakers?

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A Good Ex-Skews
It’simportant to take skew into consideration. Because the January calls
have ahigher strike price than the February calls, it’slogical for them to
trade at alower implied volatility. Is this enough to justify the possibility of
selling the lower volatility? Consider first that there is some margin for
error. The bid-ask spreads of each of the options has avolatility disparity. In
this case, both the January and February calls are 10 cents wide. That means
with a January vega of 0.34 the bid-ask is about 0.29 vol points wide. The
Februarys have a 0.57 vega. They are about 0.18 vol points wide. That
accounts for some of the disparity. Natural vertical skew accounts for the
rest of the difference, which is acceptable as long as the skew is not
abnormally pronounced.
As for other volatility considerations, this diagonal has the rather
unorthodox juxtaposition of positive vega and negative gamma seen with
other time spreads. The trader is looking for amove upward, but not abig
one. As the stock rises and Apple moves closer to the 420 strike, the
positive delta will shrink and the negative gamma will increase. In order to
continue to enjoy profits as the stock rises, John may have to buy shares of
Apple to keep his positive delta. The risk here is that if he buys stock and
Apple retraces, he may end up negative scalping stock. In other words, he
may sell it back at alower price than he bought it. Using stock to adjust the
delta in anegative-gamma play can be risky business. Gamma scalping is
addressed further in Chapter 13.

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Making the Most of Your Options
The trader from the previous example had atime-spread alternative to the
diagonal: John could have simply bought atraditional time spread at the
420 strike. Recall that calendars reap the maximum reward when they are at
the shared strike price at expiration of the short-term option. Why would he
choose one over the other?
The diagonal in that example uses alower-strike call in the February than
astraight 420 calendar spread and therefore has ahigher delta, but it costs
more. Gamma, theta, and vega may be slightly lower with the in-the-money
call, depending on how far from the strike price the ITM call is and how
much time until expiration it has. These, however, are less relevant
differences.
The delta of the February 400 call is about 0.57. The February 420 call,
however, has only a 0.39 delta. The 0.18 delta difference between the calls
means the position delta of the time spread will be only about 0.07 instead
of about 0.25 of the diagonal—abig difference. But the trade-off for lower
delta is that the February 420 call can be bought for 12.15. That means alower debit paid—that means less at risk. Conversely, though there is
greater risk with the diagonal, the bigger delta provides abigger payoff if
the trader is right.

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Double Diagonals
Adouble diagonal spread is the simultaneous trading of two diagonal
spreads: one call spread and one put spread. The distance between the
strikes is the same in both diagonals, and both have the same two expiration
months. Usually, the two long-term options are more out-of-the-money than
the two shorter-term options. For example
Buy 1 XYZ May 70 put
Sell 1 XYZ March 75 put
Sell 1 XYZ March 85 call
Buy 1 XYZ May 90 call
Like many option strategies, the double diagonal can be looked at from anumber of angles. Certainly, this is atrade composed of two diagonal
spreads—the March–May 70–75 put and the March–May 85–90 call. It is
also two strangles—buying the May 70–90 strangle and selling the March
75–85 strangle. One insightful way to look at this spread is as an iron
condor in which the guts are March options and the wings are May options.
Trading adouble diagonal like this one, rather than atypically positioned
iron condor, can offer afew advantages. The first advantage, of course, is
theta. Selling short-term options and buying long-term options helps the
trader reap higher rates of decay. Theta is the raison d’être of the iron
condor. Asecond advantage is rolling. If the underlying asset stays in arange for along period of time, the short strangle can be rolled month after
month. There may, in some cases, also be volatility-term-structure
discrepancies on which to capitalize.
Atrader, Paul, is studying JPMorgan (JPM). The current stock price is
$49.85. In this example, JPMorgan has been trading in apretty tight range
over the past few months. Paul believes it will continue to do so over the
next month. Paul considers the following trade:

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Paul considers volatility. In this example, the JPMorgan ATM call, the
August 50 (which is not shown here), is trading at 22.9 percent implied
volatility. This is in line with the 20-day historical volatility, which is 23
percent. The August IV appears to be reasonably in line with the September
volatility, after accounting for vertical skew. The IV of the August 52.50
calls is 1.5 points above that of the September 55 calls and the August 47.50
put IV is 1.6 points below the September 45 put IV. It appears that neither
month’svolatility is cheap or expensive.
Exhibit 11.12 shows the trade’sgreeks.
EXHIBIT 11.12 10-lot JPMorgan August–September 45–47.50–52.50–55
double diagonal.
The analytics of this trade are similar to those of an iron condor.
Immediate directional risk is almost nonexistent, as indicated by the delta.
But gamma and theta are high, even higher than they would be if this were
astraight September iron condor, although not as high as if this were an
August iron condor.
Vega is positive. Surely, if this were an August or a September iron
condor, vega would be negative. In this example, Paul is indifferent as to
whether vega is positive or negative because IV is fairly priced in terms of
historical volatility and term structure. In fact, to play it close to the vest,
Paul probably wants the smallest vega possible, in case of an IV move.
Why take on the risk?
The motivation for Paul’sdouble diagonal was purely theta. The
volatilities were all in line. And this one-month spread can’tbe rolled. If
Paul were interested in rolling, he could have purchased longer-term

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Direction Neutral versus Direction
Indifferent
In the world of nonlinear trading, there are two possible nondirectional
views of the underlying asset: direction neutral and direction indifferent.
Direction neutral means the trader believes the stock will not trend either
higher or lower. The trader is neutral in his or her assessment of the future
direction of the asset. Short iron condors, long time spreads, and out-of-the-
money (OTM) credit spreads are examples of direction-neutral strategies.
These strategies generally have deltas close to zero. Because of negative
gamma, movement is the bane of the direction-neutral trade.
Direction indifferent means the trader may desire movement in the
underlying but is indifferent as to whether that movement is up or down.
Some direction-indifferent trades are almost completely insulated from
directional movement, with afocus on interest or dividends instead.
Examples of these types of trades are conversions, reversals, and boxes,
which are described in Chapter 6, as well as dividend plays, which are
described in Chapter 8.
Other direction-indifferent strategies are long option strategies that have
positive gamma. In these trades, the focus is on movement, but the direction
of that movement is irrelevant. These are plays that are bullish on realized
volatility. Yet other direction-indifferent strategies are volatility plays from
the perspective of IV. These are trades in which the trader’sintent is to take
abullish or bearish position in IV.

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Delta Neutral
To be truly direction neutral or direction indifferent means to have adelta
equal to zero. In other words, there are no immediate gains if the underlying
moves incrementally higher or lower. This zero-delta method of trading is
called delta-neutral trading .
Adelta-neutral position can be created from any option position simply
by trading stock to flatten out the delta. Avery basic example of adelta-
neutral trade is along at-the-money (ATM) call with short stock.
Consider atrade in which we buy 20 ATM calls that have a 50 delta and
sell stock on adelta-neutral ratio.
Buy 20 50-delta calls (long 1,000 deltas)
Short 1,000 shares (short 1,000 deltas)
In this position, we are long 1,000 deltas from the calls (20 × 50) and
short 1,000 deltas from the short sale of stock. The net delta of the position
is zero. Therefore, the immediate directional exposure has been eliminated
from the trade. But intuitively, there are other opportunities for profit or loss
with this trade.
The addition of short stock to the calls will affect only the delta, not the
other greeks. The long calls have positive gamma, negative theta, and
positive vega. Exhibit 12.1 is asimplified representation of the greeks for
this trade.
EXHIBIT 12.1 20-lot delta-neutral long call.
With delta not an immediate concern, the focus here is on gamma, theta,
and vega. The +1.15 vega indicates that each one-point change in IV makes
or loses $115 for this trade. Yet there is more to the volatility story. Each
day that passes costs the trader $50 in time decay. Holding the position for

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an extended period of time can produce aloser even if IV rises. Gamma is
potentially connected to the success of this trade, too. If the underlying
moves in either direction, profit from deltas created by positive gamma may
offset the losses from theta. In fact, abig enough move in either direction
can produce aprofitable trade, regardless of what happens to IV.
Imagine, for amoment, that this trade is held until expiration. If the stock
is below the strike price at this point, the calls expire. The resulting position
is short 1,000 shares of stock. If the stock is above the strike price at
expiration, the calls can be exercised, creating 2,000 shares of long stock.
Because the trade is already short 1,000 shares, the resulting net position is
long 1,000 shares (2,000 − 1,000). Clearly, the more the underlying stock
moves in either direction the greater the profit potential. The underlying has
to move far enough above or below the strike price to allow the beneficial
gains from buying or selling stock to cover the option premium lost from
time decay. If the trade is held until expiration, the underlying needs to
move far enough to cover the entire premium spent on the calls.
The solid lines forming a Vin Exhibit 12.2 conceptually illustrate the
profit or loss for this delta-neutral long call at expiration.
EXHIBIT 12.2 Profit-and-loss diagram for delta-neutral long-call trade.
Because of gamma, some deltas will be created by movement of the
underlying before expiration. Gamma may lead to this being aprofitable

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Why Trade Delta Neutral?
Afew years ago, Iwas teaching aclass on option trading. Before the
seminar began, Iwas talking with one of the students in attendance. Iasked
him what he hoped to learn in the class. He said that he was really
interested in learning how to trade delta neutral. When Iasked him why he
was interested in that specific area of trading, he replied, “Ihear that’swhere all the big money is made!”
This observation, right or wrong, probably stems from the fact that in the
past most of the trading in this esoteric discipline has been executed by
professional traders. There are two primary reasons why the pros have
dominated this strategy: high commissions and high margin requirements
for retail traders. Recently, these two reasons have all but evaporated.
First, the ultracompetitive world of online brokers has driven
commissions for retail traders down to, in some cases, what some market
makers pay. Second, the oppressive margin requirements that retail option
traders were subjected to until 2007 have given way to portfolio margining.

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Portfolio Margining
Customer portfolio margining is amethod of calculating customer margin
in which the margin requirement is based on the “up and down risk” of the
portfolio. Before the advent of portfolio margining, retail traders were
subject to strategy-based margining, also called Reg. Tmargining, which in
many cases required asignificantly higher amount of capital to carry aposition than portfolio margining does.
With portfolio margining, highly correlated securities can be offset
against each other for purposes of calculating margin. For example, SPX
options and SPY options—both option classes based on the Standard &
Poor’s 500 Index—can be considered together in the margin calculation. Abearish position in one and abullish position in the other may partially
offset the overall risk of the portfolio and therefore can help to reduce the
overall margin requirement.
With portfolio margining, many strategies are margined in such away
that, from the point of view of this author, they are subject to amuch more
logical means of risk assessment. Strategy-based margining required traders
of some strategies, like aprotective put, to deposit significantly more
capital than one could possibly lose by holding the position. The old rules
require aminimum margin of 50 percent of the stock’svalue and up to 100
percent of the put premium. Aportfolio-margined protective put may
require only afraction of what it would with strategy-based margining.
Even though Reg. Tmargining is antiquated and sometimes unreasonable,
many traders must still abide by these constraints. Not all traders meet the
eligibility requirements to qualify for portfolio-based margining. There is aminimum account balance for retail traders to be eligible for this treatment.
Abroker may also require other criteria to be met for the trader to benefit
from this special margining. Ultimately, portfolio margining allows retail
traders to be margined similarly to professional traders.
There are some traders, both professional and otherwise, who indeed have
made “big money,” as the student in my class said, trading delta neutral.
But, to be sure, there are successful and unsuccessful traders in many areas

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Trading Implied Volatility
With atypical option, the sensitivity of delta overshadows that of vega. To
try and profit from arise or fall in IV, one has to trade delta neutral to
eliminate immediate directional sensitivity. There are many strategies that
can be traded as delta-neutral IV strategies simply by adding stock.
Throughout this chapter, Iwill continue using asingle option leg with
stock, since it provides asimple yet practical example. It’simportant to note
that delta-neutral trading does not refer to aspecific strategy; it refers to the
fact that the trader is indifferent to direction. Direction isn’tbeing traded,
volatility is.
Volatility trading is fundamentally different from other types of trading.
While stocks can rise to infinity or decline to zero, volatility can’t. Implied
volatility, in some situations, can rise to lofty levels of 100, 200, or even
higher. But in the long-run, these high levels are not sustainable for most
stocks. Furthermore, an IV of zero means that the options have no extrinsic
value at all. Now that we have established that the thresholds of volatility
are not as high as infinity and not as low as zero, where exactly are they?
The limits to how high or low IV can go are not lines in the sand. They are
more like tides that ebb and flow, but normally come up only so far onto the
beach.
The volatility of an individual stock tends to trade within arange that can
be unique to that particular stock. This can be observed by studying achart
of recent volatility. When IV deviates from the range, it is typical for it to
return to the range. This is called reversion to the mean , which was
discussed in Chapter 3. IV can get stretched in either direction like arubber
band but then tends to snap back to its original shape.
There are many examples of situations where reversion to the mean enters
into trading. In some, volatility temporarily dips below the typical range,
and in some, it rises beyond the recent range. One of the most common
examples is the rush and the crush.

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The Rush and the Crush
In this situation, volatility rises before and falls after awidely anticipated
news announcement, of earnings, for instance, or of a Food and Drug
Administration (FDA) approval. In this situation, option buyers rush in and
bid up IV. The more uncertainty—the more demand for insurance—the
higher vol rises. When the event finally occurs and the move takes place or
doesn’t, volatility gets crushed. The crush occurs when volatility falls very
sharply—sometimes 10 points, 20 points, or more—in minutes. Traders
with large vega positions appreciate the appropriateness of the term crush
all too well. Volatility traders also affectionately refer to this sudden drop in
IV by saying that volatility has gotten “whacked.”
In order to have afeel for whether implied volatility is high or low for aparticular stock, you need to know where it’sbeen. It’shelpful to have an
idea of where realized volatility is and has been, too. To be sure, one
analysis cannot be entirely separate from the other. Studying both implied
and realized volatility and how they relate is essential to seeing the big
picture.

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Volatility Selling
Susie Seller, avolatility trader, studies semiconductor stocks. Exhibit 12.3
shows the volatilities of a $50 chip stock. The circled area shows what
happened before and after second-quarter earnings were reported in July.
The black line is the IV, and the gray is the 30-day historical.
EXHIBIT 12.3 Chip stock volatility before and after earnings reports.
Source : Chart courtesy of iVolatility.com
In mid-July, Susie did some digging to learn that earnings were to be
announced on July 24, after the close. She was careful to observe the classic
rush and crush that occurred to varying degrees around the last three
earnings announcements, in October, January, and April. In each case, IV
firmed up before earnings only to get crushed after the report. In mid-to-late
July, she watched as IV climbed to the mid-30s (the rush) just before
earnings. As the stock lay in wait for the report, trading came to aproverbial screeching halt, sending realized volatility lower, to about 13
percent. Susie waited for the end of the day just before the report to make
her move. Before the closing bell, the stock was at $50. Susie sold 20 one-
month 50-strike calls at 2.10 (a 35 volatility) and bought 1,100 shares of the
underlying stock at $50 to become delta neutral.

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Exhibit 12.4 shows Susie’sposition.
EXHIBIT 12.4 Delta-neutral short ATM call, long stock position.
Her delta was just about flat. The delta for the 50 calls was 0.54 per
contract. Selling a 20-lot creates 10.80 short deltas for her overall position.
After buying 1,100 shares, she was left long 0.20 deltas, about the
equivalence of being long 20 shares. Where did her risk lie? Her biggest
concern was negative gamma. Without even seeing achart of the stock’sprice, we can see from the volatility chart that this stock can have big
moves on earnings. In October, earnings caused amore than 10-point jump
in realized volatility, to its highest level during the year shown. Whether the
stock rose or fell is irrelevant. Either event means risk for apremium seller.
The positive theta looks good on the surface, but in fact, theta provided
Susie with no significant benefit. Her plan was “in and out and nobody gets
hurt.” She got into the trade right before the earnings announcement and out
as soon as implied volatility dropped off. Ideally, she’dlike to hold these
types of trades for less than aday. The true prize is vega.
Susie was looking for about a 10-point drop in IV, which this option class
had following the October and January earnings reports. April had abig
drop in IV, as well, of about eight or nine points. Ultimately, what Susie is
looking for is reversion to the mean.
She gauges the normal level of volatility by observing where it is before
and after the surges caused by earnings. From early November to mid- to
late- December, the stock’s IV bounced around the 25 percent level. In the
month of February, the IV was around 25. After the drop-off following
April earnings and through much of May, the IV was closer to 20 percent.
In June, IV was just above 25. Susie surmised from this chart that when no

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earnings event is pending, this stock’soptions typically trade at about a 25
percent IV. Therefore, anticipating a 10-point decline from 35 was
reasonable, given the information available. If Susie gets it right, she stands
to make $1,150 from vega (10 points × 1.15 vegas × 100).
As we can see from the right side of the volatility chart in Exhibit 12.3 ,
Susie did get it right. IV collapsed the next morning by just more than ten
points. But she didn’tmake $1,150; she made less. Why? Realized volatility
(gamma). The jump in realized volatility shown on the graph is afunction
of the fact that the stock rallied $2 the day after earnings. Negative gamma
contributed to negative deltas in the face of arallying market. This negative
delta affected some of Susie’spotential vega profits.
So what was Susie’sprofit? On this trade she made $800. The next
morning at the open, she bought back the 50-strike calls at 2.80 (25 IV) and
sold the stock at $52. To compute her actual profit, she compared the prices
of the spread when entering the trade with the prices of the spread when
exiting. Exhibit 12.5 shows the breakdown of the trade.
EXHIBIT 12.5 Profit breakdown of delta-neutral trade.
After closing the trade, Susie knew for sure what she made or lost. But
there are many times when atrader will hold adelta-neutral position for an
extended period of time. If Susie hadn’tclosed her trade, she would have
looked at her marks to see her P&(L) at that point in time. Marks are the
prices at which the securities are trading in the actual market, either in real
time or at end of day. With most online brokers’ trading platforms or
options-trading software, real-time prices are updated dynamically and
always at their fingertips. The profit or loss is, then, calculated
automatically by comparing the actual prices of the opening transaction
with the current marks.

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What Susie will want to know is why she made $800. Why not more?
Why not less, for that matter? When trading delta neutral, especially with
more complex trades involving multiple legs, amanual computation of each
leg of the spread can be tedious. And to be sure, just looking at the profit or
loss on each leg doesn’tprovide an explanation.
Susie can see where her profits or losses came from by considering the
profit or loss for each influence contributing to the option’svalue. Exhibit
12.6 shows the breakdown.
EXHIBIT 12.6 Profit breakdown by greek.
Delta
Susie started out long 0.20 deltas. A $2 rise in the stock price yielded a $40
profit attributable to that initial delta.
Gamma
As the stock rose, the negative delta of the position increased as aresult of
negative gamma. The delta of the stock remained the same, but the negative
delta of the 50 call grew by the amount of the gamma. Deriving an exact
P&(L) attributable to gamma is difficult because gamma is adynamic
metric: as the stock price changes, so can the gamma. This calculation
assumes that gamma remains constant. Therefore, the gamma calculation
here provides only an estimate.
The initial position gamma of −1.6 means the delta decreases by 3.2 with
a $2 rise in the stock (–1.60 times the $2 rise in the stock price). Susie, then,
would multiply −3.2 by $2 to find the loss on −3.2 deltas over a $2 rise. But
she wasn’tshort 3.2 deltas for the whole $2. She started out with zero deltas
attributable to gamma and ended up being 3.2 shorter from gamma over that
$2 move. Therefore, if she assumes her negative delta from gamma grew
steadily from 0 to −3.2, she can estimate her average delta loss over that
move by dividing by 2.

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The Imprecision of Estimation
It is important to notice that the P&(L) found by adding up the P&(L)’sfrom the greeks is slightly different from the actual P&(L). There are acouple of reasons for this. First, the change in delta resulting from gamma is
only an estimate, because gamma changes as the stock price changes. For
small moves in the underlying, the gamma change is less significant, but for
larger moves, the rate of change of the gamma can be bigger, and it can be
nonlinear. For example, as an option moves from being at-the-money
(ATM) to being out-of-the-money (OTM), its gamma decreases. But as the
option becomes more OTM, its gamma decreases at aslower rate.
Another reason that the P&(L) from the greeks is different from the actual
P&(L) is that the greeks are derived from the option-pricing model and are
therefore theoretical values and do not include slippage.
Furthermore, the volatility input in this example is rounded abit for
simplicity. For example, avolatility of 25 actually yielded atheoretical
value of 2.796, while the call was bought at 2.80. Because some options
trade at minimum price increments of anickel, and none trade in fractions
of apenny, IV is often rounded.

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Volatility Buying
This same earnings event could have been played entirely differently. Adifferent trader, Bobby Buyer, studied the same volatility chart as Susie. It
is shown again here as Exhibit 12.7 . Bobby also thought there would be arush and crush of IV, but he decided to take adifferent approach.
EXHIBIT 12.7 Chip stock volatility before and after earnings reports.
Source : Chart courtesy of iVolatility.com
About an hour before the close of business on July 21, just three days
before earnings announcements, Bobby saw that he could buy volatility at
30 percent. In Bobby’sopinion, volatility seemed cheap with earnings so
close. He believed that IV could rise at least five points over the next three
days. Note that we have the benefit of 20/20 hindsight in the example.
Near the end of the trading day, the stock was at $49.70. Bobby bought 20
33-day 50-strike calls at 1.75 (30 volatility) and sold short 1,000 shares of
the underlying stock at $49.70 to become delta neutral. Exhibit 12.8 shows
Bobby’sposition.

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EXHIBIT 12.8 Delta-neutral long call, short stock position.
With the stock at $49.70, the calls had +0.51 delta per contract, or +10.2
for the 20-lot. The short sale of 1,000 shares got Bobby as close to delta-
neutral as possible without trading an odd lot in the stock. The net position
delta was +0.20, or about the equivalent of being long 20 shares of stock.
Bobby’sobjective in this case is to profit from an increase in implied
volatility leading up to earnings.
While Susie was looking for reversion to the mean, Bobby hoped for afurther divergence. For Bobby, positive gamma looked like agood thing on
the surface. However, his plan was to close the position just before earnings
were released—before the vol crush and before the potential stock-price
move. With realized volatility already starting to drop off at the time the
trade was put on, gamma offered little promise of gain.
As fate would have it, IV did indeed increase. At the end of the day before
the July earnings report, IV was trading at 35 percent. Bobby closed his
trade by selling his 20-lot of the 50 calls at 2.10 and buying his 1,000 shares
of stock back at $50. Exhibit 12.9 shows the P&(L) for each leg of the
spread.
EXHIBIT 12.9 Profit breakdown.

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The calls earned Bobby atotal of $700, while the stock lost $300. Of
course, with this type of trade, it is not relevant which leg was awinner and
which aloser. All that matters is the bottom line. The net P&(L) on the trade
was again of $400. The gain in this case was mostly aproduct of IV’srising. Exhibit 12.10 shows the P&(L) per greek.
EXHIBIT 12.10 Profit breakdown by greek.
Delta
The position began long 0.20 deltas. The 0.30-point rise earned Bobby a
0.06 point gain in delta per contract.
Gamma
Bobby had an initial gamma of +1.8. We will use 1.8 for estimating the P&
(L) in this example, assuming gamma remained constant. A 0.30 rise in the
stock price multiplied by the 1.8 gamma means that with the stock at $50,
Bobby was long an additional 0.54 deltas. We can estimate that over the
course of the 0.30 rise in the stock price, Bobby was long an average of
0.27 (0.54 ÷ 2). His P&(L) due to gamma, therefore, is again of about 0.08
(0.27 × 0.30).
Theta
Bobby held this trade for three days. His total theta cost him 1.92 or $192.
Vega
The biggest contribution to Bobby’sprofit on this trade was made by the
spike in IV. He bought 30 volatility and sold 35 volatility. His 1.20 position
vega earned him 6.00, or $600.

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Trading Realized Volatility
So far, we’ve discussed many option strategies in which realized volatility
is an important component of the trade. And while the management of these
positions has been the focus of much of the discussion, the ultimate gain or
loss for many of these strategies has been from movement in asingle
direction. For example, with along call, the higher the stock rallies the
better.
But increases or decreases in realized volatility do not necessarily have an
exclusive relationship with direction. Recall that realized volatility is the
annualized standard deviation of daily price movements. Take two similarly
priced stocks that have had anet price change of zero over aone-month
period. Stock Ahad small daily price changes during that period, rising
$0.10 one day and falling $0.10 the next. Stock Bwent up or down by $5
each day for amonth. In this rather extreme example, Stock Bwas much
more volatile than Stock A, regardless of the fact that the net price change
for the period for both stocks was zero.
Astock’svolatility—either high or low volatility—can be capitalized on
by trading options delta neutral. Simply put, traders buy options delta
neutral when they believe astock will have more movement and sell
options delta neutral when they believe astock will move less.
Delta-neutral option sellers profit from low volatility through theta. Every
day that passes in which the loss from delta/gamma movement is less than
the gain from theta is awinning day. Traders can adjust their deltas by
hedging. Delta-neutral option buyers exploit volatility opportunities through
atrading technique called gamma scalping.

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Gamma Scalping
Intraday trading is seldom entirely in one direction. Astock may close
higher or lower, even sharply higher or lower, on the day, but during the day
there is usually not asteady incremental rise or fall in the stock price. Atypical intraday stock chart has peaks and troughs all day long. Delta-
neutral traders who have gamma don’tremain delta neutral as the
underlying price changes, which inevitably it will. Delta-neutral trading is
kind of amisnomer.
In fact, it is gamma trading in which delta-neutral traders engage. For
long-gamma traders, the position delta gets more positive as the underlying
moves higher and more negative as the underlying moves lower. An upward
move in the underlying increases positive deltas, resulting in exponentially
increasing profits. But if the underlying price begins to retrace downward,
the gain from deltas can be erased as quickly as it was racked up.
To lock in delta gains, atrader can adjust the position to delta neutral
again by selling short stock to cover long deltas. If the stock price declines
after this adjustment, losses are curtailed thanks to the short stock. In fact,
the delta will become negative as the underlying price falls, leading to
growing profits. To lock in profits again, the trader buys stock to cover
short deltas to once again become delta neutral.
The net effect is astock scalp. Positive gamma causes the delta-neutral
trader to sell stock when the price rises and buy when the stock falls. This
adds up to atrue, realized profit. So positive gamma is amoney-making
machine, right? Not so fast. As in any business, the profits must be great
enough to cover expenses. Theta is the daily cost of running this gamma-
scalping business.
For example, atrader, Harry, notices that the intraday price swings in aparticular stock have been increasing. He takes abullish position in realized
volatility by buying 20 off the 40-strike calls, which have a 50 delta, and
selling stock on adelta-neutral ratio.
Buy 20 40-strike calls (50 delta) (long 1,000 deltas)
Short 1,000 shares at $40 (short 1,000 deltas)

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The immediate delta of this trade is flat, but as the stock moves up or
down, that will change, presenting gamma-scalping opportunities. Gamma
scalping is the objective here. The position greeks in Exhibit 13.1 show the
relationship of the two forces involved in this trade: gamma and theta.
EXHIBIT 13.1 Greeks for 20-lot delta-neutral long call.
The relationship of gamma to theta in this sort of trade is paramount to its
success. Gamma-scalping plays are not buy-and-hold strategies. This is
active trading. These spreads need to be monitored intraday to take
advantage of small moves in the underlying security. Harry will sell stock
when the underlying rises and buy it when the underlying falls, taking aprofit with each stock trade. The goal for each day that passes is to profit
enough from positive gamma to cover the day’stheta. But that’snot always
as easy as it sounds. Let’sstudy what happens the first seven days after this
hypothetical trade is executed. For the purposes of this example, we assume
that gamma remains constant and that the trader is content trading odd lots
of stock.

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Day One
The first day proves to be fairly volatile. The stock rallies from $40 to $42
early in the day. This creates apositive position delta of 5.60, or the
equivalent of being long about 560 shares. At $42, Harry covers the
position delta by selling 560 shares of the underlying stock to become delta
neutral again.
Later in the day, the market reverses, and the stock drops back down to
$40 ashare. At this point, the position is short 5.60 deltas. Harry again
adjusts the position, buying 560 shares to get flat. The stock then closes
right at $40.
The net result of these two stock transactions is again of $1,070. How?
The gamma scalp minus the theta, as shown below.
The volatility of day one led to it being aprofitable day. Harry scalped 560
shares for a $2 profit, resulting from volatility in the stock. If the stock
hadn’tmoved as much, the delta would have been smaller, and the dollar
amount scalped would have been smaller, leading to an exponentially
smaller profit. If there had been more volatility, profits would have been
exponentially larger. It would have led to abigger bite being taken out of
the market.

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Day Three
On this day, the market trends. First, the stock rises $0.50, at which point
Harry sells 140 shares of stock at $40.50 to lock in gains from his delta and
to get flat. However, the market continues to rally. At $41 ashare, Harry is
long another 1.40 deltas and so sells another 140 shares. The rally
continues, and at $41.50 he sells another 140 shares to cover the delta.
Finally, at the end of the day, the stock closes at $42 ashare. Harry sells afinal 140 shares to get flat.
There was not any literal scalping of stock today. It was all selling.
Nonetheless, gamma trading led to aprofitable day.
As the stock rose from $40 to $40.50, 140 deltas were created from
positive gamma. Because the delta was zero at $40 and 140 at $40.50, the
estimated average delta is found by dividing 140 in half. This estimated
average delta multiplied by the $0.50 gain on the stock equals a $35 profit.
The delta was zero after the adjustment made at $40.50, when 140 shares
were sold. When the stock reached $41, another $35 was reaped from the
average delta of 70 over the $0.50 move. This process was repeated every
time the stock rose $0.50 and the delta was covered.

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Art and Science
Although this was avery simplified example, it was typical of how aprofitable week of gamma scalping plays out. This stock had apretty
volatile week, and overall the week was awinner: there were four losing
days and three winners. The number of losing days includes the weekends.
Weekends and holidays are big hurdles for long-gamma traders because of
the theta loss. The biggest contribution to this being awinning week was
made by the gap open on day four. Part of the reason was the sheer
magnitude of the move, and part was the fact that the deltas weren’tcovered
too soon, as they had been on day three.
In aperfect world, along-gamma trader will always buy the low of the
day and sell the high of the day when covering deltas. This, unfortunately,
seldom happens. Long-gamma traders are very often wrong when trading
stock to cover deltas.
Being wrong can be okay on occasion. In fact, it can even be rewarding.
Day three was profitable despite the fact that 140 shares were sold at
$40.50, $41, and $41.50. The stock closed at $42; the first three stock trades
were losers. Harry sold stock at alower price than the close. But the
position still made money because of his positive gamma. To be sure, Harry
would like to have sold all 560 shares at $42 at the end of the day. The day’sprofits would have been significantly higher.
The problem is that no one knows where the stock will move next. On
day three, if the stock had topped out at $40.50 and Harry did not sell stock
because he thought it would continue higher, he would have missed an
opportunity. Gamma scalping is not an exact science. The art is to pick
spots that capture the biggest moves possible without missing opportunities.
There are many methods traders have used to decide where to cover
deltas when gamma scalping: the daily standard deviation, afixed
percentage of the stock price, afixed nominal value, covering at acertain
time of day, “market feel.” No system appears to be absolutely better than
another. This is where it gets personal. Finding what works for you, and
what works for the individual stocks you trade, is the art of this science.

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Gamma, Theta, and Volatility
Clearly, more volatile stocks are more profitable for gamma scalping, right?
Well . . . maybe. Recall that the higher the implied volatility, the lower the
gamma and the higher the theta of at-the-money (ATM) options. In many
cases, the more volatile astock, the higher the implied volatility (IV). That
means that avolatile stock might have to move more for atrader to scalp
enough stock to cover the higher theta.
Let’slook at the gamma-theta relationship from another perspective. In
this example, for 0.50 of theta, Harry could buy 2.80 gamma. This
relationship is based on an assumed 25 percent implied volatility. If IV were
50 percent, theta for this 20 lot would be higher, and the gamma would be
lower. At avolatility of 50, Harry could buy 1.40 gammas for 0.90 of theta.
The gamma is more expensive from atheta perspective, but if the stock’sstatistical volatility is significantly higher, it may be worth it.

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Gamma Hedging
Knowing that the gamma and theta figures of Exhibit 13.1 are derived from
a 25 percent volatility assumption offers abenchmark with which to gauge
the potential profitability of gamma trading the options. If the stock’sstandard deviation is below 25 percent, it will be difficult to make money
being long gamma. If it is above 25 percent, the play becomes easier to
trade. There is more scalping opportunity, there are more opportunities for
big moves, and there are more likely to be gaps in either direction. The 25
percent volatility input not only determines the option’stheoretical value
but also helps determine the ratio of gamma to theta.
A 25 percent or higher realized volatility in this case does not guarantee
the trade’ssuccess or failure, however. Much of the success of the trade has
to do with how well the trader scalps stock. Covering deltas too soon leads
to reduced profitability. Covering too late can lead to missed opportunities.
Trading stock well is also important to gamma sellers with the opposite
trade: sell calls and buy stock delta neutral. In this example, atrader will
sell 20 ATM calls and buy stock on adelta-neutral ratio.
This is abearish position in realized volatility. It is the opposite of the
trade in the last example. Consider again that 25 percent IV is the
benchmark by which to gauge potential profitability. Here, if the stock’svolatility is below 25, the chances of having aprofitable trade are increased.
Above 25 is abit more challenging.
In this simplified example, adifferent trader, Mary, plays the role of
gamma seller. Over the same seven-day period as before, instead of buying
calls, Mary sold a 20 lot. Exhibit 13.2 shows the analytics for the trade. For
the purposes of this example, we assume that gamma remains constant and
the trader is content trading odd lots of stock.

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Day One
This was one of the volatile days. The stock rallied from $40 to $42 early in
the day and had fallen back down to $40 by the end of the day. Big moves
like this are hard to trade as ashort-gamma trader. As the stock rose to $42,
the negative delta would have been increasing. That means losses were
adding up at an increasing rate. The only way to have stopped the
hemorrhaging of money as the stock continued to rise would have been to
buy stock. Of course, if Mary buys stock and the stock then declines, she
has aloser.
Let’sassume the best-case scenario. When the stock reached $42 and she
had a −560 delta, Mary correctly felt the market was overbought and would
retrace. Sometimes, the best trades are the ones you don’tmake. On this
day, Mary traded no stock. When the stock reached $40 ashare at the end of
the day, she was back to being delta neutral. Theta makes her awinner
today.
Because of the way Mary handled her trade, the volatility of day one was
not necessarily an impediment to it being profitable. Again, the assumption
is that Mary made the right call not to negative scalp the stock. Mary could
have decided to hedge her negative gamma when the stock reach $42 and
the position delta was at −$560 by buying stock and then selling it at $40.
There are anumber of techniques for hedging deltas resulting from
negative gamma. The objective of hedging deltas is to avoid losses from the
stock trending in one direction and creating increasingly adverse deltas but
not to overtrade stock and negative scalp.

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Day Three
Day three saw the stock price trending. It slowly drifted up $2. There would
have been some judgment calls throughout this day. Again, delta-neutral
trades are for active traders. Prepare to watch the market much of the day if
implementing this kind of strategy.
When the stock was at $41 ashare, Mary decided to guard against further
advances in stock price and hedged her delta. At that point, the position
would have had a −2.80 delta. She bought 280 shares at $41.
As the day progressed, the market proved Mary to be right. The stock rose
to $42 giving the position adelta of −2.80 again. She covered her deltas at
the end of the day by buying another 280 shares.
Covering the negative deltas to get flat at $41 proved to be asmart move
today. It curtailed an exponentially growing delta and let Mary take asmaller loss at $41 and get afresh start. While the day was aloser, it would
have been $280 worse if she had not purchased stock at $41 before the run-
up to $42. This is evidenced by the fact that she made a $280 profit on the
280 shares of stock bought at $41, since the stock closed at $42.

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Day Four
Day four offered arather unpleasant surprise. This was the day that the
stock gapped open $4 lower. This is the kind of day short-gamma traders
dread. There is, of course, no right way to react to this situation. The stock
can recover, heading higher; it can continue lower; or it can have adead-cat
bounce, remaining where it is after the fall.
Staring at aquite contrary delta of 11.20, Mary was forced to take action
by selling stock. But how much stock was the responsible amount to sell for
apure short-gamma trader not interested in trading direction? Selling 1,120
shares would bring the position back to being delta neutral, but the only
way the trade would stay delta neutral would be if the stock stayed right
where it was.
Hedging is always adifficult call for short-gamma traders. Long-gamma
traders are taking aprofit on deltas with every stock trade that covers their
deltas. Short-gamma traders are always taking aloss on delta. In this case,
Mary decided to cover half her deltas by selling 560 shares. The other 560
deltas represent aloss, too; it’sjust not locked in.
Here, Mary made the conscious decision not to go home flat. On the one
hand, she was accepting the risk of the stock continuing its decline. On the
other hand, if she had covered the whole delta, she would have been
accepting the risk of the stock moving in either direction. Mary felt the
stock would regain some of its losses. She decided to lead the stock alittle,
going into the weekend with apositive delta bias.

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Day Seven
This was the quiet day of the week, and awelcome respite. On this day, the
stock rose just $0.25. The rise in price helped abit. Mary was still long 560
deltas from Friday. Negative gamma took only asmall bite out of her profit.
The P&(L) can be broken down into the profit attributable to the starting
delta of the trade, the estimated loss from gamma, and the gain from theta.
Mary ends these seven days of trading worse off than she started. What
went wrong? The bottom line is that she sold volatility on an asset that
proved to be volatile. A $4 drop in price of a $42 dollar stock was abig
move. This stock certainly moved at more than 25 percent volatility. Day
four alone made this trade alosing proposition.
Could Mary have done anything better? Yes. In aperfect world, she
would not have covered her negative deltas on day 3 by buying 280 shares
at $41 and another 280 at $42. Had she not, this wouldn’thave been such abad week. With the stock ending at $38.25, she lost $1,050 on the 280
shares she bought at $42 ($3.75 times 280) and lost $770 on the 280 shares
bought at $41 ($2.75 times 280). Then again, if the stock had continued
higher, rising beyond $42, those would have been good buys.
Mary can’tbeat herself up too much for protecting herself in away that
made sense at the time. The stock’s $2 rally is more to blame than the fact
that she hedged her deltas. That’sthe risk of selling volatility: the stock may
prove to be volatile. If the stock had not made such amove, she wouldn’thave faced the dilemma of whether or not to hedge.

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Conclusions
The same stock during the same week was used in both examples. These
two traders started out with equal and opposite positions. They might as
well have made the trade with each other. And although in this case the vol
buyer (Harry) had apretty good week and the vol seller (Mary) had anot-
so-good week, it’simportant to notice that the dollar value of the vol
buyer’sprofit was not the same as the dollar value of the vol seller’sloss.
Why? Because each trader hedged his or her position differently. Option
trading is not azero-sum game.
Option-selling delta-neutral strategies work well in low-volatility
environments. Small moves are acceptable. It’sthe big moves that can blow
you out of the water.
Like long-gamma traders, short-gamma traders have many techniques for
covering deltas when the stock moves. It is common to cover partial deltas,
as Mary did on day four of the last example. Conversely, if astock is
expected to continue along its trajectory up or down, traders will sometimes
overhedge by buying more deltas (stock) than they are short or selling more
than they are long, in anticipation of continued price rises. Daily standard
deviation derived from implied volatility is acommon measure used by
short-gamma players to calculate price points at which to enter hedges.
Market feel and other indicators are also used by experienced traders when
deciding when and how to hedge. Each trader must find what works best for
him or her.

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Smileys and Frowns
The trade examples in this chapter have all involved just two components:
calls and stock. We will explore delta-neutral strategies in other chapters
that involve more moving parts. Regardless of the specific makeup of the
position, the P&(L) of each individual leg is not of concern. It is the
profitability of the position as awhole that matters. For example, after avolatile move in astock occurs, apositive-gamma trader like Harry doesn’tcare whether the calls or the stock made the profit on the move. The trader
would monitor the net delta that was produced—positive or negative—and
cover accordingly. The process is the same for anegative-gamma trader. In
either case, it is gamma and delta that need to be monitored closely.
Gamma can make or break atrade. P&(L) diagrams are helpful tools that
offer avisual representation of the effect of gamma on aposition. Many
option-trading software applications offer P&(L) graphing applications to
study the payoff of aposition with the days to expiration as an adjustable
variable to study the same trade over time.
P&(L) diagrams for these delta-neutral positions before the options’
expiration generally take one of two shapes: asmiley or afrown. The shape
of the graph depends on whether the position gamma is positive or negative.
Exhibit 13.3 shows atypical positive-gamma trade.

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EXHIBIT 13.4 The effect of time on P&(L).
As time passes, the reduction in profit is reflected by the center point of
the graph dipping farther into negative territory. That is the effect of time
decay. The long options will have lost value at that future date with the
stock still at the same price (all other factors held constant). Still, amove in
either direction can lead to aprofitable position. Ultimately, at expiration,
the payoff takes on arigid kinked shape.
In the delta-neutral long call examples used in this chapter the position
becomes net long stock if the calls are in-the-money at expiration or net
short stock if they are out-of-the-money and only the short stock remains.
Volatility, as well, would move the payoff line vertically. As IV increases,
the options become worth more at each stock price, and as IV falls, they are
worth less, assuming all other factors are held constant.
Adelta-neutral short-gamma play would have a P&(L) diagram quite the
opposite of the smiley-faced long-gamma graph. Exhibit 13.5 shows what is
called the short-gamma frown.

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Adecrease in value of the options from time decay causes an increase in
profitability. This profit potential pinnacles at the center (strike) price at
expiration. Rising IV will cause adecline in profitability at each stock price
point. Declining IV will raise the payout on the Yaxis as profitability
increases at each price point.
Smileys and frowns are amere graphical representation of the technique
discussed in this chapter: buying and selling realized volatility. These P&
(L) diagrams are limited, because they show the payout only of stock-price
movement. The profitability of direction-indifferent and direction-neutral
trading is also influenced by time and implied volatility. These actively
traded strategies are best evaluated on agamma-theta basis. Long-gamma
traders strive each day to scalp enough to cover the day’stheta, while short-
gamma traders hope to keep the loss due to adverse movement in the
underlying lower than the daily profit from theta.
The strategies in this chapter are the same ones traded in Chapter 12. The
only difference is the philosophy. Ultimately, both types of volatility are
being traded using these and other option strategies. Implied and realized
volatility go hand in hand.

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CHAPTER 14
Studying Volatility Charts
Implied and realized volatility are both important to option traders. But
equally important is to understand how the two interact. This relationship is
best studied by means of avolatility chart. Volatility charts are invaluable
tools for volatility traders (and all option traders for that matter) in many
ways.
First, volatility charts show where implied volatility (IV) is now
compared with where it’sbeen in the past. This helps atrader gauge
whether IV is relatively high or relatively low. Vol charts do the same for
realized volatility. The realized volatility line on the chart answers three
questions:
Have the past 30 days been more or less volatile for the stock than
usual?
What is atypical range for the stock’svolatility?
How much volatility did the underlying historically experience in the
past around specific recurring events?
When IV lines and realized volatility lines are plotted on the same chart,
the divergences and convergences of the two spell out the whole volatility
story for those who know how to read it.

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1. Realized Volatility Rises, Implied
Volatility Rises
The first volatility chart pattern is that in which both IV and realized
volatility rise. In general, this kind of volatility chart can line up three ways:
implied can rise more than realized volatility; realized can rise more than
implied; or they can both rise by about the same amount. The chart below
shows implied volatility rising at afaster rate than realized vol. The general
theme in this case is that the stock’sprice movement has been getting more
volatile, and the option prices imply even higher volatility in the future.
This specific type of volatility chart pattern is commonly seen in active
stocks with alot of news. Stocks du jour, like some Internet stocks during
the tech bubble of the late 1990s, story stocks like Apple (AAPL) around
the release of the iPhone in 2007, have rising volatilities, with the IV
outpacing the realized volatility. Sometimes individual stocks and even
broad market indexes and exchange-traded funds (ETFs) see this pattern,
when the market is declining rapidly, like in the summer of 2011.
Adelta-neutral long-volatility position bought at the beginning of May,
according to Exhibit 14.1 , would likely have produced awinner. IV took
off, and there were sure to be plenty of opportunities to profit from gamma
with realized volatility gaining strength through June and July.
EXHIBIT 14.1 Realized volatility rises, implied volatility rises.
Source : Chart courtesy of iVolatility.com

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Looking at the right side of the chart, in late July, with IV at around 50
percent and realized vol at around 35 percent, and without the benefit of
knowing what the future will bring, it’sharder to make acall on how to
trade the volatility. The IV signals that the market is pricing ahigher future
level of stock volatility into the options. If the market is right, gamma will
be good to have. But is the price right? If realized volatility does indeed
catch up to implied volatility—that is, if the lines converge at 50 or realized
volatility rises above IV—atrader will have agood shot at covering theta.
If it doesn’t, gamma will be very expensive in terms of theta, meaning it
will be hard to cover the daily theta by scalping gamma intraday.
The question is: why is IV so much higher than realized? If important
news is expected to be released in the near future, it may be perfectly
reasonable for the IV to be higher, even significantly higher, than the
stock’srealized volatility. One big move in the stock can produce anice
profit, as long as theta doesn’thave time to work its mischief. But if there is
no news in the pipeline, there may be some irrational exuberance—in the
words of ex-Fed chairman Alan Greenspan—of option buyers rushing to
acquire gamma that is overvalued in terms of theta.
In fact, alack of expectation of news could indicate apotential bearish
volatility play: sell volatility with the intent of profiting from daily theta
and adecline in IV. This type of play, however, is not for the fainthearted.
No one can predict the future. But one thing you can be sure of with this

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trade: you’re in for awild ride. The lines on this chart scream volatility.
This means that negative-gamma traders had better be good and had better
be right!
In this situation, hedgers and speculators in the market are buying option
volatility of 50 percent, while the stock is moving at 35 percent volatility.
Traders putting on adelta-neutral volatility-selling strategy are taking the
stance that this stock will not continue increasing in volatility as indicated
by option prices; specifically, it will move at less than 50 percent volatility
—hopefully alot less. They are taking the stance that the market’sexpectations are wrong.
Instead of realized and implied volatility both trending higher, sometimes
there is asharp jump in one or the other. When this happens, it could be an
indication of aspecific event that has occurred (realized volatility) or news
suddenly released of an expected event yet to come (implied volatility). Asharp temporary increase in IV is called aspike, because of its pointy shape
on the chart. Aone-day surge in realized volatility, on the other hand, is not
so much avolatility spike as it is arealized volatility mesa. Realized
volatility mesas are shown in Exhibit 14.2 .
EXHIBIT 14.2 Volatility mesas.
Source : Chart courtesy of iVolatility.com
The patterns formed by the gray line in the circled areas of the chart
shown below are the result of typical one-day surges in realized volatility.

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2. Realized Volatility Rises, Implied
Volatility Remains Constant
This chart pattern can develop from afew different market conditions. One
scenario is aone-time unanticipated move in the underlying that is not
expected to affect future volatility. Once the news is priced into the stock,
there is no point in hedgers’ buying options for protection or speculators’
buying options for aleveraged bet. What has happened has happened.
There are other conditions that can cause this type of pattern to
materialize. In Exhibit 14.3 , the IV was trading around 25 for several
months, while the realized volatility was lagging. With hindsight, it makes
perfect sense that something had to give—either IV needed to fall to meet
realized, or realized would rise to meet market expectations. Here, indeed,
the latter materialized as realized volatility had asteady rise to and through
the 25 level in May. Implied, however remained constant.
EXHIBIT 14.3 Realized volatility rises, implied volatility remains
constant.
Source : Chart courtesy of iVolatility.com
Traders who were long volatility going into the May realized-vol rise
probably reaped some gamma benefits. But those who got in “too early,”
buying in January or February, would have suffered too great of theta losses
before gaining any significant profits from gamma. Time decay (theta) can
inflict aslow, painful death on an option buyer. By studying this chart in
hindsight, it is clear that options were priced too high for agamma scalper
to have afighting chance of covering the daily theta before the rise in May.

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3. Realized Volatility Rises, Implied
Volatility Falls
This chart pattern can manifest itself in different ways. In this scenario, the
stock is becoming more volatile, and options are becoming cheaper. This
may seem an unusual occurrence, but as we can see in Exhibit 14.4 ,
volatility sometimes plays out this way. This chart shows two different
examples of realized vol rising while IV falls.
EXHIBIT 14.4 Realized volatility rises, implied volatility falls.
Source : Chart courtesy of iVolatility.com
The first example, toward the left-hand side of the chart, shows realized
volatility trending higher while IV is trending lower. Although
fundamentals can often provide logical reasons for these volatility changes,
sometimes they just can’t. Both implied and realized volatility are
ultimately afunction of the market. There is anormal oscillation to both of
these figures. When there is no reason to be found for avolatility change, it
might be an opportunity. The potential inefficiency of volatility pricing in
the options market sometimes creates divergences such as this one that vol
traders scour the market in search of.
In this first example, after at least three months of IV’strading marginally
higher than realized volatility, the two lines converge and then cross. The

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point at which these lines meet is an indication that IV may be beginning to
get cheap.
First, it’sapotentially beneficial opportunity to buy alower volatility than
that at which the stock is actually moving. The gamma/theta ratio would be
favorable to gamma scalpers in this case, because the lower cost of options
compared with stock fluctuations could lead to gamma profits. Second, with
IV at 35 at the first crossover on this chart, IV is dipping down into the
lower part of its four-month range. One can make the case that it is getting
cheaper from ahistorical IV standpoint. There is arguably an edge from the
perspective of IV to realized volatility and IV to historical IV. This is an
example of buying value in the context of volatility.
Furthermore, if the actual stock volatility is rising, it’sreasonable to
believe that IV may rise, too. In hindsight we see that this did indeed occur
in Exhibit 14.4 , despite the fact that realized volatility declined.
The example circled on the right-hand side of the chart shows IV
declining sharply while realized volatility rises sharply. This is an example
of the typical volatility crush as aresult of an earnings report. This would
probably have been agood trade for long volatility traders—even those
buying at the top. Atrader buying options delta neutral the day before
earnings are announced in this example would likely lose about 10 points of
vega but would have agood chance to more than make up for that loss on
positive gamma. Realized volatility nearly doubled, from around 28 percent
to about 53 percent, in asingle day.

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4. Realized Volatility Remains Constant,
Implied Volatility Rises
Exhibit 14.5 shows that the stock is moving at about the same volatility
from the beginning of June to the end of July. But during that time, option
premiums are rising to higher levels. This is an atypical chart pattern. If this
was aperiod leading up to an anticipated event, like earnings, one would
anticipate realized volatility falling as the market entered await-and-see
mode. But, instead, statistical volatility stays the same. This chart pattern
may indicate apotential volatility-selling opportunity. If there is no news or
reason for IV to have risen, it may simply be high tide in the normal ebb
and flow of volatility.
EXHIBIT 14.5 Realized volatility remains constant, implied volatility
rises.
Source : Chart courtesy of iVolatility.com
In this example, the historical volatility oscillates between 20 and 24 for
nearly two months (the beginning of June through the end of July) as IV
rises from 24 to over 30. The stock price is less volatile than option prices
indicate. If there is no news to be dug up on the stock to lead one to believe
there is avalid reason for the IV’strading at such alevel, this could be an
opportunity to sell IV 5 to 10 points higher than the stock volatility. The

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5. Realized Volatility Remains Constant,
Implied Volatility Remains Constant
This volatility chart pattern shown in Exhibit 14.6 is typical of aboring,
run-of-the-mill stock with nothing happening in the news. But in this case,
no news might be good news.
EXHIBIT 14.6 Realized volatility remains constant, implied volatility
remains constant.
Source : Chart courtesy of iVolatility.com
Again, the gray is realized volatility and the black line is IV.
It’scommon for IV to trade slightly above or below realized volatility for
extended periods of time in certain assets. In this example, the IV has traded
in the high teens from late January to late July. During that same time,
realized volatility has been in the low teens.
This is aprime environment for option sellers. From agamma/theta
standpoint, the odds favor short-volatility traders. The gamma/theta ratio
provides an edge, setting the stage for theta profits to outweigh negative-
gamma scalping. Selling calls and buying stock delta neutral would be atrade to look at in this situation. But even more basic strategies, such as
time spreads and iron condors, are appropriate to consider.

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6. Realized Volatility Remains Constant,
Implied Volatility Falls
Exhibit 14.7 shows two classic implied-realized convergences. From mid-
September to early November, realized volatility stayed between 22 and 25.
In mid-October the implied was around 33. Within the span of afew days,
the implied vol collapsed to converge with the realized at about 22.
EXHIBIT 14.7 Realized volatility remains constant, implied volatility falls.
Source : Chart courtesy of iVolatility.com
There can be many catalysts for such adrop in IV, but there is truly only
one reason: arbitrage. Although it is common for asmall difference between
implied and realized volatility—1 to 3 points—to exist even for extended
periods, bigger disparities, like the 7- to 10-point difference here cannot
exist for that long without good reason.
If, for example, IV always trades significantly above the realized
volatility of aparticular underlying, all rational market participants will sell
options because they have agamma/theta edge. This, in turn, forces options
prices lower until volatility prices come into line and the arbitrage
opportunity no longer exists.
In Exhibit 14.7 , from mid-March to mid-May asimilar convergence took
place but over alonger period of time. These situations are often the result

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7. Realized Volatility Falls, Implied
Volatility Rises
This setup shown in Exhibit 14.8 should now be etched into the souls of
anyone who has been reading up to this point. It is, of course, the picture of
the classic IV rush that is often seen in stocks around earnings time. The
more uncertain the earnings, the more pronounced this divergence can be.
EXHIBIT 14.8 Realized volatility falls, implied volatility rises.
Source : Chart courtesy of iVolatility.com
Another classic vol divergence in which IV rises and realized vol falls
occurs in adrug or biotech company when a Food and Drug Administration
(FDA) decision on one of the company’snew drugs is imminent. This is
especially true of smaller firms without big portfolios of drugs. These
divergences can produce ahuge implied–realized disparity of, in some
cases, literally hundreds of volatility points leading up to the
announcement.
Although rising IV accompanied by falling realized volatility can be one
of the most predictable patterns in trading, it is ironically one of the most
difficult to trade. When the anticipated news breaks, the stock can and often
will make abig directional move, and in that case, IV can and likely will
get crushed. Vega and gamma work against each other in these situations, as

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8. Realized Volatility Falls, Implied
Volatility Remains Constant
This volatility shift can be marked by avolatility convergence, divergence,
or crossover. Exhibit 14.9 shows the realized volatility falling from around
30 percent to about 23 percent while IV hovers around 25. The crossover
here occurs around the middle of February.
EXHIBIT 14.9 Realized volatility falls, implied volatility remains constant.
Source : Chart courtesy of iVolatility.com
The relative size of this volatility change makes the interpretation of the
chart difficult. The last half of September saw around a 15 percent decline
in realized volatility. The middle of October saw aone-day jump in realized
of about 15 points. Historical volatility has had several dynamic moves that
were larger and more abrupt than the seven-point decline over this six-week
period. This smaller move in realized volatility is not necessarily an
indication of avolatility event. It could reflect some complacency in the
market. It could indicate aslow period with less trading, or it could simply
be anatural contraction in the ebb and flow of volatility causing the
calculation of recent stock-price fluctuations to wane.
What is important in this interpretation is how the options market is
reacting to the change in the volatility of the stock—where the rubber hits

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the road. The market’sapparent assessment of future volatility is unchanged
during this period. When IV rises or falls, vol traders must look to the
underlying stock for areason. The options market reacts to stock volatility,
not the other way around.
Finding fundamental or technical reasons for surges in volatility is easier
than finding specific reasons for adecline in volatility. When volatility falls,
it is usually the result of alack of news, leading to less price action. In this
example, probably nothing happened in the market. Consequently, the stock
volatility drifted lower. But it fell below the lowest IV level seen for the six-
month period leading up to the crossover. It was probably hard to take aconfident stance in volatility immediately following the crossover. It is
difficult to justify selling volatility when the implied is so cheap compared
with its historic levels. And it can be hard to justify buying volatility when
the options are priced above the stock volatility.
The two-week period before the realized line moved beneath the implied
line deserves closer study. With the IV four or five points lower than the
realized volatility in late January, traders may have been tempted to buy
volatility. In hindsight, this trade might have been profitable, but there was
surely no guarantee of this. Success would have been greatly contingent on
how the traders managed their deltas, and how well they adapted as realized
volatility fell.
During the first half of this period, the stock volatility remained above
implied. For an experienced delta-neutral trader, scalping gamma was likely
easy money. With the oscillations in stock price, the biggest gamma-
scalping risk would have been to cover too soon and miss out on
opportunities to take bigger profits.
Using the one-day standard deviation based on IV (described in Chapter
3) might have produced early covering for long-gamma traders. Why?
Because in late January, the standard deviation derived from IV was lower
than the actual standard deviation of the stock being traded. In the latter half
of the period being studied, the end of February on this chart, using the one-
day standard deviation based on IV would have produced scalping that was
too late. This would have led to many missed opportunities.
Traders entering hedges at regular nominal intervals—every $0.50, for
example—would probably have needed to decrease the interval as volatility

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9. Realized Volatility Falls, Implied
Volatility Falls
This final volatility-chart permutation incorporates afall of both realized
and IV. The chart in Exhibit 14.10 clearly represents the slow culmination
of ahighly volatile period. This setup often coincides with news of some
scary event’sbeing resolved—alaw suit settled, unpopular upper
management leaving, rumors found to be false, ahappy ending to political
issues domestically or abroad, for example. After asharp sell-off in IV,
from 75 to 55, in late October, marking the end of aperiod of great
uncertainty, the stock volatility began asteady decline, from the low 50s to
below 25. IV fell as well, although it remained abit higher for several
months.
EXHIBIT 14.10 Realized volatility falls, implied volatility falls.
Source : Chart courtesy of iVolatility.com
In some situations where an extended period of extreme volatility appears
to be coming to an end, there can be some predictability in how IV will
react. To be sure, no one knows what the future holds, but when volatility
starts to wane because aspecific issue that was causing gyrations in the
stock price is resolved, it is common, and intuitive, for IV to fall with the
stock volatility. This is another type of example of reversion to the mean.

eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:419


The Basic Long Straddle
The long straddle is an option strategy to use when atrader is looking for abig move in astock but is uncertain which direction it will move.
Technically, the Commodity Channel Index (CCI), Bollinger bands, or
pennants are some examples of indicators which might signal the possibility
of abreakout. Or fundamental data might call for arevaluation of the stock
based on an impending catalyst. In either case, along straddle, is away for
traders to position themselves for the expected move, without regard to
direction. In this example, we’ll study ahypothetical $70 stock poised for abreakout. We’ll buy the one-month 70 straddle for 4.25.
Exhibit 15.1 shows the payout of the straddle at expiration.
EXHIBIT 15.1 At-expiration diagram for along straddle.
At expiration, with the stock at $70, neither the call nor the put is in-the-
money. The straddle expires worthless, leaving aloss of 4.25 in its wake
from erosion. If, however, the stock is above or below $70, either the call or
the put will have at least some value. The farther the stock price moves

eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:425