option
matching the market price.
For a specific stock price, a given implied volatility will yield a unique
option value. Take a stock trading at $44.22 that has the 60-day 45-strike
call at a theoretical value of $1.10 with an 18 percent implied volatility
level. If the stock price remains constant, but IV rises to 19 percent, the
value of the call will rise by its vega, which in this case is about 0.07. The
new value of the call will be $1.17. Raising IV another point, to 20 percent,
raises the theoretical value by another $0.07, to $1.24. The question is:
What would cause implied volatility to change?
Supply and Demand: Not Just a Good
Idea, It’s the Law!
Options are an excellent vehicle for speculation. However, the existence of
the options market is better justified by the primary economic purpose of
options: as a risk management tool. Hedgers use options to protect their
assets from adverse price movements, and when the perception of risk
increases, so does demand for this protection. In this context, risk means
volatility—the potential for larger moves to the upside and downside. The
relative prices of options are driven higher by increased demand for
protective options when the market anticipates greater volatility. And option
prices are driven lower by greater supply—that is, selling of options—when
the market expects lower volatility. Like those of all assets, option prices
are subject to the law of supply and demand.
When volatility is expected to rise, demand for options is not limited to
hedgers. Speculative traders would arguably be more inclined to buy a call
than to buy the stock if they are bullish but expect future volatility to be
high. Calls require a lower cash outlay. If the stock moves adversely, there
is less capital at risk, but still similar profit potential.
When volatility is expected to be low, hedging investors are less inclined
to pay for protection. They are more likely to sell back the options they may
have bought previously to recoup some of the expense. Options are a
decaying asset. Investors are more likely to write calls against stagnant
stocks to generate income in anticipated low-volatility environments.
Speculative traders will implement option-selling strategies, such as short
strangles or iron condors, in an attempt to capitalize on stocks they believe
won’t move much. The rising supply of options puts downward pressure on
option prices.
Many traders sum up IV in two words: fear and greed . When option
prices rise and fall, not because of changes in the stock price, time to
expiration, interest rates, or dividends, but because of pure supply and
demand, it is implied volatility that is the varying factor. There are many
contributing factors to traders’ willingness to demand or supply options.
Anticipation of events such as earnings reports, Federal Reserve
announcements, or the release of other news particular to an individual
stock can cause anxiety, or fear, in traders and consequently increase
demand for options that causes IV to rise. IV can fall when there is
complacency in the market or when the anticipated news has been
announced and anxiety wanes. “Buy the rumor, sell the news” is often
reflected in option implied volatility. When there is little fear of market
movement, traders use options to squeeze out more profits—greed.
Arbitrageurs, such as market makers who trade delta neutral—a strategy
that will be discussed further in Chapters 12 and 13—must be relentlessly
conscious of implied volatility. When immediate directional risk is
eliminated from a position, IV becomes the traded commodity. Arbitrageurs
who focus their efforts on trading volatility (colloquially called vol traders )
tend to think about bids and offers in terms of IV. In the mind of a vol
trader, option prices are translated into volatility levels. A trader may look at
a particular option and say it is 30 bid at 31 offer. These values do not
represent the prices of the options but rather the corresponding implied
volatilities. The meaning behind the trader’s remark is that the market is
willing to buy implied volatility at 30 percent and sell it at 31 percent. The
actual prices of the options themselves are much less relevant to this type of
trader.
Should HV and IV Be the Same?
Most option positions have exposure to volatility in two ways. First, the
profitability of the position is usually somewhat dependent on movement
(or lack of movement) of the underlying security. This is exposure to HV.
Second, profitability can be affected by changes in supply and demand for
the options. This is exposure to IV. In general, a long option position
benefits when volatility—both historical and implied—increases. A short
option position benefits when volatility—historical and implied—decreases.
That said, buying options is buying volatility and selling options is selling
volatility.
The Relationship of HV and IV
It’s intuitive that there should exist a direct relationship between the HV and
IV. Empirically, this is often the case. Supply and demand for options, based
on the market’s expectations for a security’s volatility, determines IV.
It is easy to see why IV and HV often act in tandem. But, although HV
and IV are related, they are not identical. There are times when IV and HV
move in opposite directions. This is not so illogical, if one considers the key
difference between the two: HV is calculated from past stock price
movements; it is what has happened. IV is ultimately derived from the
market’s expectation for future volatility.
If a stock typically has an HV of 30 percent and nothing is expected to
change, it can be reasonable to expect that in the future the stock will
continue to trade at a 30 percent HV. By that logic, assuming that nothing is
expected to change, IV should be fairly close to HV. Market conditions do
change, however. These changes are often regular and predictable. Earnings
reports are released once a quarter in many stocks, Federal Open Market
Committee


ing is expected to
change, it can be reasonable to expect that in the future the stock will
continue to trade at a 30 percent HV. By that logic, assuming that nothing is
expected to change, IV should be fairly close to HV. Market conditions do
change, however. These changes are often regular and predictable. Earnings
reports are released once a quarter in many stocks, Federal Open Market
Committee meetings happen regularly, and dates of other special
announcements are often disclosed to the public in advance. Although the
outcome of these events cannot be predicted, when they will occur often
can be. It is around these widely anticipated events that HV-IV divergences
often occur.
HV-IV Divergence
An HV-IV divergence occurs when HV declines and IV rises or vice versa.
The classic example is often observed before a company’s quarterly
earnings announcement, especially when there is lack of consensus among
analysts’ estimates. This scenario often causes HV to remain constant or
decline while IV rises. The reason? When there is a great deal of
uncertainty as to what the quarterly earnings will be, investors are reluctant
to buy or sell the stock until the number is released. When this happens, the
stock price movement (volatility) consolidates, causing the calculated HV
to decline. IV, however, can rise as traders scramble to buy up options—
bidding up their prices. When the news is out, the feared (or hoped for)
move in the stock takes place (or doesn’t), and HV and IV tend to converge
again.
Expected Volatility
Whether trading options or stocks, simple or complex strategies, traders
must consider volatility. For basic buy-and-hold investors, taking a potential
investment’s volatility into account is innate behavior. Do I buy
conservative (nonvolatile) stocks or more aggressive (volatile) stocks?
Taking into account volatility, based not just on a gut feeling but on hard
numbers, can lead to better, more objective trading decisions.
Expected Stock Volatility
Option traders must have an even greater focus on volatility, as it plays a
much bigger role in their profitability—or lack thereof. Because options can
create highly leveraged positions, small moves can yield big profits or
losses. Option traders must monitor the likelihood of movement in the
underlying closely. Estimating what historical volatility (standard deviation)
will be in the future can help traders quantify the probability of movement
beyond a certain price point. This leads to better decisions about whether to
enter a trade, when to adjust a position, and when to exit.
There is no way of knowing for certain what the future holds. But option
data provide traders with tools to develop expectations for future stock
volatility. IV is sometimes interpreted as the market’s estimate of the future
volatility of the underlying security. That makes it a ready-made estimation
tool, but there are two caveats to bear in mind when using IV to estimate
future stock volatility.
The first is that the market can be wrong. The market can wrongly price
stocks. This mispricing can lead to a correction (up or down) in the prices
of those stocks, which can lead to additional volatility, which may not be
priced in to the options. Although there are traders and academics believe
that the option market is fairly efficient in pricing volatility, there is a room
for error. There is the possibility that the option market can be wrong.
Another caveat is that volatility is an annualized figure—the annualized
standard deviation. Unless the IV of a LEAPS option that has exactly one
year until expiration is substituted for the expected volatility of the
underlying stock over exactly one year, IV is an incongruent estimation for
the future stock volatility. In practice, the IV of an option must be adjusted
to represent the period of time desired.
There is a common technique for deannualizing IV used by professional
traders and retail traders alike. 1 The first step in this process to deannualize
IV is to turn it into a one-day figure as opposed to one-year figure. This is
accomplished by dividing IV by the square root of the number of trading
days in a year. The number many traders use to approximate the number of
trading days per year is 256, because its square root is a round number: 16.
The formula is
For example, a $100 stock that has an at-the-money (ATM) call trading at
a 32 percent volatility implies that there is about a 68 percent chance that
the underlying stock will be between $68 and $132 in one year’s time—
that’s $100 ± ($100 × 0.32). The estimation for the market’s expectation for
the volatility of the stock for one day in terms of standard deviation as a
percentage of the price of the underlying is computed as follows:
In one day’s time, based on an IV of 32 percent, there is a 68 percent
chance of the stock’s being within 2 percent of the stock price—that’s
between $98 and $102.
There may be times when it is helpful for traders to have a volatility
estimation for a period of time longer than one day—a week or a month, for
example. This can be accomplished by multiplying the one-day volatility by
the square root of the number of trading days in the relevant period. The
equation is as follows:
If the period in question is one month and there are 22 business days
remaining in that month, the same $100 stock with the ATM call trading at a
32 percent implied volatility would have a one-month volatility of 9.38
percent.
Based on this calculation for one month, it can be estimated that there is a
68 percent chance of the stock’s closing between $90.62 and $109.38 based
on an IV of 32 percent.
Expected Implied Volatility
Although there is a great deal of science that can be applied to calculating
expected actual volatility, developing expectations for implied volatility is
more of an art. This element of an option’s price provides more risk and
more opportunity. There are many traders who make their living distilling
direction out of their positions

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


109.38 based
on an IV of 32 percent.
Expected Implied Volatility
Although there is a great deal of science that can be applied to calculating
expected actual volatility, developing expectations for implied volatility is
more of an art. This element of an option’s price provides more risk and
more opportunity. There are many traders who make their living distilling
direction out of their positions and trading implied volatility. To be
successful, a trader must forecast IV.
Conceptually, trading IV is much like trading anything else. A trader who
thinks a stock is going to rise will buy the stock. A trader who thinks IV is
going to rise will buy options. Directional stock traders, however, have
many more analysis tools available to them than do vol traders. Stock
traders have both technical analysis (TA) and fundamental analysis at their
disposal.
Technical Analysis
There are scores, perhaps hundreds, of technical tools for analyzing stocks,
but there are not many that are available for analyzing IV. Technical
analysis is the study of market data, such as past prices or volume, which is
manipulated in such a way that it better illustrates market activity. TA
studies are usually represented graphically on a chart.
Developing TA tools for IV is more of a challenge than it is for stocks.
One reason is that there is simply a lot more data to manage—for each
stock, there may be hundreds of options listed on it. The only practical way
of analyzing options from a TA standpoint is to use implied volatility. IV is
more useful than raw historical option prices themselves. Information for
both IV and HV is available in the form of volatility charts, or vol charts.
(Vol charts are discussed in detail in Chapter 14.) Volatility charts are
essential for analyzing options because they give more complete
information.
To get a clear picture of what is going on with the price of an option (the
goal of technical analysis for any asset), just observing the option price does
not supply enough information for a trader to work with. It’s incomplete.
For example, if a call rises in value, why did it rise? What greek contributed
to its value increase? Was it delta because the underlying stock rose? Or
was it vega because volatility rose? How did time decay factor in? Using a
volatility chart in conjunction with a conventional stock chart (and being
aware of time decay) tells the whole, complete, story.
Another reason historical option prices are not used in TA is the option
bid-ask spread. For most stocks, the difference between the bid and the ask
is equal to a very small percentage of the stock’s price. Because options are
highly leveraged instruments, their bid-ask width can equal a much higher
percentage of the price.
If a trader uses the last trade to graph an option’s price, it could look as if
a very large percentage move has occurred when in fact it has not. For
example, if the option trades a small contract size on the bid (0.80), then on
the offer (0.90) it would appear that the option rose 12.5 percent in value.
This large percentage move is nothing more than market noise. Using
volatility data based off the midpoint-of-the-market theoretical value
eliminates such noise.
Fundamental Analysis
Fundamental analysis can have an important role in developing
expectations for IV. Fundamental analysis is the study of economic factors
that affect the value of an asset in order to determine what it is worth. With
stocks, fundamental analysis may include studying income statements,
balance sheets, and earnings reports. When the asset being studied is IV,
there are fewer hard facts available. This is where the art of analyzing
volatility comes into play.
Essentially, the goal is to understand the psychology of the market in
relation to supply and demand for options. Where is the fear? Where is the
complacency? When are news events anticipated? How important are they?
Ultimately, the question becomes: what is the potential for movement in the
underlying? The greater the chance of stock movement, the more likely it is
that IV will rise. When unexpected news is announced, IV can rise quickly.
The determination of the fundamental relevance of surprise announcements
must be made quickly.
Unfortunately, these questions are subjective in nature. They require the
trader to apply intuition and experience on a case-by-case basis. But there
are a few observations to be made that can help a trader make better-
educated decisions about IV.
Reversion to the Mean
The IVs of the options on many stocks and indexes tend to trade in a range
unique to those option classes. This is referred to as the mean—or average
—volatility level. Some securities will have smaller mean IV ranges than
others. The range being observed should be established for a period long
enough to confirm that it is a typical IV for the security, not just a
temporary anomaly. Traders should study IV over the most recent 6-month
period. When IV has changed significantly during that period, a 12-month
study may be necessary. Deviations from this range, either above or below
the established mean range, will occur from time to time. When following a
breakout from the established range, it is common for IV to revert back to
its normal range. This is commonly called reversion to the mean among
volatility watchers.
The challenge is recognizing when things change and when they stay the
same. If the fundamentals of the stock change in such a way as to give the
options market reason to believe the stock will now be more or less volatile
on an ongoing basis than it typically has been in the recent past, the IV may
not revert to the mean. Instead, a new mean volatility level may be
established.
When considering the likelihood of whether IV will revert to recent levels
after it has deviated or find a new range, the time horizon and changes in
the marketplace must be taken into account. For example, between 1998
and 2003 the mean volatility level of the SPX was around 20 percen


n in the recent past, the IV may
not revert to the mean. Instead, a new mean volatility level may be
established.
When considering the likelihood of whether IV will revert to recent levels
after it has deviated or find a new range, the time horizon and changes in
the marketplace must be taken into account. For example, between 1998
and 2003 the mean volatility level of the SPX was around 20 percent to 30
percent. By the latter half of 2006, the mean IV was in the range of 10
percent to 13 percent. The difference was that between 1998 and 2003 was
the buildup of “the tech bubble,” as it was called by the financial media.
Market volatility ultimately leveled off in 2003.
In a later era, between the fall of 2010 and late summer of 2011 SPX
implied volatility settled in to trade mostly between 12 and 20 percent. But
in August 2011, as the European debt crisis heated up, a new, more volatile
range between 24 and 40 percent reigned for some time.
No trader can accurately predict future IV any more than one can predict
the future price of a stock. However, with IV there are often recurring
patterns that traders can observe, like the ebb and flow of IV often
associated with earnings or other regularly scheduled events. But be aware
that the IV’s rising before the last 15 earnings reports doesn’t mean it will
this time.
CBOE Volatility Index
®
Often traders look to the implied volatility of the market as a whole for
guidance on the IV of individual stocks. Traders use the Chicago Board
Options Exchange (CBOE) Volatility Index® , or VIX® , as an indicator of
overall market volatility.
When people talk about the market, they are talking about a broad-based
index covering many stocks on many diverse industries. Usually, they are
referring to the S&P 500. Just as the IV of a stock may offer insight about
investors’ feelings about that stock’s future volatility, the volatility of
options on the S&P 500—SPX options—may tell something about the
expected volatility of the market as a whole.
VIX is an index published by the Chicago Board Options Exchange that
measures the IV of a hypothetical 30-day option on the SPX. A 30-day
option on the SPX only truly exists once a month—30 days before
expiration. CBOE computes a hypothetical 30-day option by means of a
weighted average of the two nearest-term months.
When the S&P 500 rises or falls, it is common to see individual stocks
rise and fall in sympathy with the index. Most stocks have some degree of
market risk. When there is a perception of higher risk in the market as a
whole, there can consequently be a perception of higher risk in individual
stocks. The rise or fall of the IV of SPX can translate into the IV of
individual stocks rising or falling.
Implied Volatility and Direction
Who’s afraid of falling stock prices? Logically, declining stocks cause
concern for investors in general. There is confirmation of that statement in
the options market. Just look at IV. With most stocks and indexes, there is
an inverse relationship between IV and the underlying price. Exhibit 3.2
shows the SPX plotted against its 30-day IV, or the VIX.
EXHIBIT 3.2 SPX vs. 30-day IV (VIX).
The heavier line is the SPX, and the lighter line is the VIX. Note that as
the price of SPX rises, the VIX tends to decline and vice versa. When the
market declines, the demand for options tends to increase. Investors hedge
by buying puts. Traders speculate on momentum by buying puts and
speculate on a turnaround by buying calls. When the market moves higher,
investors tend to sell their protection back and write covered calls or cash-
secured puts. Option speculators initiate option-selling strategies. There is
less fear when the market is rallying.
This inverse relationship of IV to the price of the underlying is not unique
to the SPX; it applies to most individual stocks as well. When a stock
moves lower, the market usually bids up IV, and when the stock rises, the
market tends to offer IV creating downward pressure.
Calculating Volatility Data
Accurate data are essential for calculating volatility. Many of the volatility
data that are readily available are useful, but unfortunately, some are not.
HV is a value that is easily calculated from publicly accessible past closing
prices of a stock. It’s rather straightforward. Traders can access HV from
many sources. Retail traders often have access to HV from their brokerage
firm. Trading firms or clearinghouses often provide professional traders
with HV data. There are some excellent online resources for HV as well.
HV is a calculation with little subjectivity—the numbers add up how they
add up. IV, however, can be a bit more ambiguous. It can be calculated
different ways to achieve different desired outcomes; it is user-centric. Most
of the time, traders consider the theoretical value to be between the bid and
the ask prices. On occasion, however, a trader will calculate IV for the bid,
the ask, the last trade price, or, sometimes, another value altogether. There
may be a valid reason for any of these different methods for calculating IV.
For example, if a trader is long volatility and aspires to reduce his position,
calculating the IV for the bid shows him what IV level can be sold to
liquidate his position.
Firms, online data providers, and most options-friendly brokers offer IV
data. Past IV data is usually displayed graphically in what is known as a
volatility chart or vol chart. Current IV is often displayed along with other
data right in the option chain. One note of caution: when the current IV is
displayed, however, it should always be scrutinized carefully. Was the bid
used in calculating this figure? What about the ask? How long ago was this
calculation made? There are many questions that determine the accuracy of
a current IV, and rarely are there any answers to support the number.
Traders should trust only IV data they knowingly generated themselves
using a pricing model.
Volatility Skew
There are many platforms (software or Web-ba


ized carefully. Was the bid
used in calculating this figure? What about the ask? How long ago was this
calculation made? There are many questions that determine the accuracy of
a current IV, and rarely are there any answers to support the number.
Traders should trust only IV data they knowingly generated themselves
using a pricing model.
Volatility Skew
There are many platforms (software or Web-based) that enable traders to
solve for volatility values of multiple options within the same option class.
Values of options of the same class are interrelated. Many of the model
parameters are shared among the different series within the same class. But
IV can be different for different options within the same class. This is
referred to as the volatility skew . There are two types of volatility skew:
term structure of volatility and vertical skew.
Term Structure of Volatility
Term structure of volatility—also called monthly skew or horizontal skew
—is the relationship among the IVs of options in the same class with the
same strike but with different expiration months. IV, again, is often
interpreted as the market’s estimate of future volatility. It is reasonable to
assume that the market will expect some months to be more volatile than
others. Because of this, different expiration cycles can trade at different IVs.
For example, if a company involved in a major product-liability lawsuit is
expecting a verdict on the case to be announced in two months, the one-
month IV may be low, as the stock is not expected to move much until the
suit is resolved. The two-month volatility may be much higher, however,
reflecting the expectations of a big move in the stock up or down,
depending on the outcome.
The term structure of volatility also varies with the normal ebb and flow
of volatility within the business cycle. In periods of declining volatility, it is
common for the month with the least amount of time until expiration, also
known as the front month, to trade at a lower volatility than the back
months, or months with more time until expiration. Conversely, when
volatility is rising, the front month tends to have a higher IV than the back
months.
Exhibit 3.3 shows historical option prices and their corresponding IVs for
32.5-strike calls on General Motors (GM) during a period of low volatility.
EXHIBIT 3.3 GM term structure of volatility.
In this example, no major news is expected to be released on GM, and
overall market volatility is relatively low. The February 32.5 call has the
lowest IV, at 32 percent. Each consecutive month has a higher IV than the
previous month. A graduated increasing or decreasing IV for each
consecutive expiration cycle is typical of the term structure of volatility.
Under normal circumstances, the front month is the most sensitive to
changes in IV. There are two reasons for this. First, front-month options are
typically the most actively traded. There is more buying and selling
pressure. Their IV is subject to more activity. Second, vegas are smaller for
options with fewer days until expiration. This means that for the same
monetary change in an option’s value, the IV needs to move more for short-
term options.
Exhibit 3.4 shows the same GM options and their corresponding vegas.
EXHIBIT 3.4 GM vegas.
If the value of the September 32.5 calls increases by $0.10, IV must rise
by 1 percentage point. If the February 32.5 calls increase by $0.10, IV must
rise 3 percentage points. As expiration approaches, the vega gets even
smaller. With seven days until expiration, the vega would be about 0.014.
This means IV would have to change about 7 points to change the call value
$0.10.
Vertical Skew
The second type of skew found in option IV is vertical skew, or strike skew.
Vertical skew is the disparity in IV among the strike prices within the same
month for an option class. The options on most stocks and indexes
experience vertical skew. As a general rule, the IV of downside options—
calls and puts with strike prices lower than the at-the-money (ATM) strike
—trade at higher IVs than the ATM IV. The IV of upside options—calls and
puts with strike prices higher than the ATM strike—typically trade at lower
IVs than the ATM IV.
The downside is often simply referred to as puts and the upside as calls.
The rationale for this lingo is that OTM options (puts on the downside and
calls on the upside) are usually more actively traded than the ITM options.
By put-call parity, a put can be synthetically created from a call, and a call
can be synthetically created from a put simply by adding the appropriate
long or short stock position.
Exhibit 3.5 shows the vertical skew for 86-day options on Citigroup Inc.
(C) on a typical day, with IVs rounded to the nearest tenth.
EXHIBIT 3.5 Citigroup vertical skew.
Notice the IV of the puts (downside options) is higher than that of the
calls (upside options), with the 31 strike’s volatility more than 10 points
higher than that of the 38 strike. Also, the difference in IV per unit change
in the strike price is higher for the downside options than it is for the upside
ones. The difference between the IV of the 31 strike is 2 full points higher
than the 32 strike, which is 1.8 points higher than the 33 strike. But the 36
strike’s IV is only 1.1 points higher than the 37 strike, which is also just 1.1
points higher than the 38 strike.
This incremental difference in the IV per strike is often referred to as the
slope. The puts of most underlyings tend to have a greater slope to their
skew than the calls. Many models allow values to be entered for the upside
slope and the downside slope that mathematically increase or decrease IVs
of each strike incrementally. Some traders believe the slope should be a
straight line, while others believe it should be an exponentially sloped line.
If the IVs were graphed, the shape of the skew would vary among asset
classes. This is sometimes referred to as the volatility smile or sneer,
depending on the shape of the IV skew. Although


nside slope that mathematically increase or decrease IVs
of each strike incrementally. Some traders believe the slope should be a
straight line, while others believe it should be an exponentially sloped line.
If the IVs were graphed, the shape of the skew would vary among asset
classes. This is sometimes referred to as the volatility smile or sneer,
depending on the shape of the IV skew. Although Exhibit 3.5 is a typical
paradigm for the slope for stock options, bond options and other commodity
options would have differently shaped skews. For example, grain options
commonly have calls with higher IVs than the put IVs.
Volatility skew is dependent on supply and demand. Greater demand for
downside protection may cause the overall IV to rise, but it can cause the
IV of puts to rise more relative to the calls or vice versa. There are many
traders who make their living trading volatility skew.
Note
1 . This technique provides only an estimation of future volatility.
CHAPTER 4
Option-Specific Risk and Opportunity
New endeavors can be intimidating. The first day at a new job or new
school is a challenge. Option trading is no different. When traders first
venture into the world of options, they tend to start with what they know—
trading direction. Buying stocks is at the heart of the comfort zone for many
traders. Buying a call as a substitute for buying a stock is a logical
progression. And for the most part, call buying is a pretty straightforward
way to take a bullish position in a stock. But it’s not just a bullish position.
The greeks come into play with the long call, providing both risk and
opportunity.
Long ATM Call
Kim is a trader who is bullish on the Walt Disney Company (DIS) over the
short term. The time horizon of her forecast is three weeks. Instead of
buying 100 shares of Disney at $35.10 per share, Kim decides to buy one
Disney March 35 call at $1.10. In this example, March options have 44
days until expiration. How can Kim profit from this position? How can she
lose?
Exhibit 4.1 shows the profit and loss (P&(L)) for the call at different time
periods. The top line is when the trade is executed; the middle, dotted line is
after three weeks have passed; and the bottom, darker line is at expiration.
Kim wants Disney to rise in price, which is evident by looking at the graph
for any of the three time horizons. She would anticipate a loss if the stock
price declines. These expectations are related to the position’s delta, but that
is not the only risk exposure Kim has. As indicated by the three different
lines in Exhibit 4.1 , the call loses value over time. This is called theta risk .
She has other risk exposure as well. Exhibit 4.2 lists the greeks for the DIS
March 35 call.
EXHIBIT 4.1 P&(L) of Disney 35 call.
EXHIBIT 4.2 Greeks for 35 Disney call.
Delta 0.57
Gamma0.166
Theta −0.013
Vega 0.048
Rho 0.023
Kim’s immediate directional exposure is quantified by the delta, which is
0.57. Delta is immediate directional exposure because it’s subject to change
by the amount of the gamma. The positive gamma of this position helps
Kim by increasing the delta as Disney rises and decreasing it as it falls.
Kim, however, has time working against her—theta. At this point, she
theoretically loses $0.013 per day. Since her call is close to being at-the-
money, she would anticipate her theta becoming more negative as
expiration approaches if Disney’s share price remains unchanged. She also
has positive vega exposure. A one-percentage-point increase in implied
volatility (IV) earns Kim just under $0.05. A one-point decrease costs her
about $0.05. With so few days until expiration, the 35-strike call has very
little rho exposure. A full one-percentage-point change in the interest rate
changes her call’s value by only $0.023.
Delta
Some of Kim’s risks warrant more concern than others. With this position,
delta is of the greatest concern, followed by theta. Kim expects the call to
rise in value and accepts the risk of decline. Delta exposure was her main
rationale for establishing the position. She expects to hold it for about three
weeks. Kim is willing to accept the trade-off of delta exposure for theta,
which will cost her three weeks of erosion of option premium. If the
anticipated delta move happens sooner than expected, Kim will have less
decay. Exhibit 4.3 shows the value of her 35 call at various stock prices
over time. The left column is the price of Disney. The top row is the number
of days until expiration.
EXHIBIT 4.3 Disney 35 call price–time matrix–value.
The effect of delta is evident as the stock rises or falls. When the position
is established (44 days until expiration), the change in the option price if the
stock were to move from $35 to $36 is 0.62 (1.66 − 1.04). Between stock
prices of $36 and $37, the option gains 0.78 (2.44 −1.66). If the stock were
to decline in value from $35 to $34, the option loses 0.47 (1.04 − 0.57). The
option gains value at a faster rate as the stock rises and loses value at a
slower rate as the stock falls. This is the effect of gamma.
Gamma
With this type of position, gamma is an important but secondary
consideration. Gamma is most helpful to Kim in developing expectations of
what the delta will be as the stock price rises or falls. Exhibit 4.4 shows the
delta at various stock prices over time.
EXHIBIT 4.4 Disney call price–time matrix–delta.
Kim pays attention to gamma only to gauge her delta. Why is this
important to her? In this trade, Kim is focused on direction. Knowing how
much her call will rise or fall in step with the stock is her main concern.
Notice that her delta tends to get bigger as the stock rises and smaller as the
stock falls. As time passes, the delta gravitates toward 1.00 or 0, depending
on whether the call is in-the-money (ITM) or out-of-the-money (OTM).
Theta
Option buying is a veritable race against the clock. With each passing day,
the option loses theoretical value. Refer back to Exhibit 4.3 . When three
weeks pass and the time t


at her delta tends to get bigger as the stock rises and smaller as the
stock falls. As time passes, the delta gravitates toward 1.00 or 0, depending
on whether the call is in-the-money (ITM) or out-of-the-money (OTM).
Theta
Option buying is a veritable race against the clock. With each passing day,
the option loses theoretical value. Refer back to Exhibit 4.3 . When three
weeks pass and the time to expiration decreases from 44 days to 23, what
happens to the call value? If the stock price stays around its original level,
theta will be responsible for a loss of about 30 percent of the premium. If
Disney is at $35 with 23 days to expiration, the call will be worth $0.73.
With a big enough move in either direction, however, theta matters much
less.
With 23 days to expiration and Disney at $39, there is only 0.12 of time
value—the premium paid over parity for the option. At that point, it is
almost all delta exposure. Similarly, if the Disney stock price falls after
three weeks to $33, the call will have only 0.10 of time value. Time decay is
the least of Kim’s concerns if the stock makes a big move.
Vega
After delta and theta, vega is the next most influential contributor to Kim’s
profit or peril. With Disney at $35.10, the 1.10 premium for the 35-strike
call represents $1 of time value—all of which is vulnerable to changes in
IV. The option’s 1.10 value returns an IV of about 19 percent, given the
following inputs:
Stock: $35.10
Strike: 35
Days to expiration: 44
Interest: 5.25 percent
No dividend paid during this period
Consequently, the vega is 0.048. What does the 0.048 vega tell Kim?
Given the preceding inputs, for each point the IV rises or falls, the option’s
value gains or loses about $0.05.
Some of the inputs, however, will change. Kim anticipates that Disney
will rise in price. She may be right or wrong. Either way, it is unlikely that
the stock will remain exactly at $35.10 to option expiration. The only
certainty is that time will pass.
Both price and time will change Kim’s vega exposure. Exhibit 4.5 shows
the changing vega of the 35 call as time and the underlying price change.
EXHIBIT 4.5 Disney 35 call price–time matrix–vega.
When comparing Exhibit 4.5 to Exhibit 4.3 , it’s easy to see that as the
time value of the option declines, so does Kim’s exposure to vega. As time
passes, vega gets smaller. And as the call becomes more in- or out-of-the-
money, vega gets smaller. Since she plans to hold the position for around
three weeks, she is not concerned about small fluctuations in IV in the
interim.
If indeed the rise in price that Kim anticipates comes to pass, vega
becomes even less of a concern. With 23 days to expiration and DIS at $37,
the call value is 2.21. The vega is $0.018. If IV decreases as the stock price
rises—a common occurrence—the adverse effect of vega will be minimal.
Even if IV declines by 5 points, to a historically low IV for DIS, the call
loses less than $0.10. That’s less than 5 percent of the new value of the
option.
If dividend policy changes or the interest rate changes, the value of Kim’s
call will be affected as well. Dividends are often fairly predictable.
However, a large unexpected dividend payment can have a significant
adverse impact on the value of the call. For example, if a surprise $3
dividend were announced, owning the stock would become greatly
preferable to owning the call. This preference would be reflected in the call
premium. This is a scenario that an experienced trader like Kim will realize
is a possibility, although not a probability. Although she knows it can
happen, she will not plan for such an event unless she believes it is likely to
happen. Possible reasons for such a belief could be rumors or the
company’s historically paying an irregular dividend.
Rho
For all intents and purposes, rho is of no concern to Kim. In recent years,
interest rate changes have not been a major issue for option traders. In the
Alan Greenspan years of Federal Reserve leadership, changes in the interest
rate were usually announced at the regularly scheduled Federal Open
Market Committee (FOMC) meetings, with but a few exceptions. Ben
Bernanke, likewise, changed interest rates fairly predictably, when he made
any rate changes at all. In these more stable periods, if there is no FOMC
meeting scheduled during the life of the call, it’s unlikely that rates will
change. Even if they do, the rho with 44 days to expiration is only 0.023.
This means that if rates change by a whole percentage point—which is four
times the most common incremental change—the call value will change by
a little more than $0.02. In this case, this is an acceptable risk. With 23 days
to expiration, the ATM 35 call has a rho of only 0.011.
Tweaking Greeks
With this position, some risks are of greater concern than others. Kim may
want more exposure to some greeks and less to others. What if she is
concerned that her forecasted price increase will take longer than three
weeks? She may want less exposure to theta. What if she is particularly
concerned about a decline in IV? She may want to decrease her vega.
Conversely, she may believe IV will rise and therefore want to increase her
vega.
Kim has many ways at her disposal to customize her greeks. All of her
alternatives come with trade-offs. She can buy more calls, increasing her
greek positions in exact proportion. She can buy or sell stock or options
against her call, creating a spread. The simplest way to alter her exposure to
option greeks is to choose a different call to buy. Instead of buying the ATM
call, Kim can buy a call with a different relationship to the current stock
price.
Long OTM Call
Kim can reduce her exposure to theta and vega by buying an OTM call. The
trade-off here is that she also reduces her immediate delta exposure.
Depending on how much Kim believes Disney will rally, this may or may
not be a viable trade-off. Imagine that instead of buying one Disney March
35 call, Kim buys one Disney March 37.50 call, for 0.20


t relationship to the current stock
price.
Long OTM Call
Kim can reduce her exposure to theta and vega by buying an OTM call. The
trade-off here is that she also reduces her immediate delta exposure.
Depending on how much Kim believes Disney will rally, this may or may
not be a viable trade-off. Imagine that instead of buying one Disney March
35 call, Kim buys one Disney March 37.50 call, for 0.20.
There are a few observations to be made about this alternative position.
First, the net premium, and therefore overall risk, is much lower, 0.20
instead of 1.10. From an expiration standpoint, the breakeven at expiration
is $37.70 (the strike price plus the call premium). Since Kim plans on
exiting the position after about three weeks, the exact break-even point at
the expiration of the contract is irrelevant. But the concept is the same: the
stock needs to rise significantly. Exhibit 4.6 shows how Kim’s concerns
translate into greeks.
EXHIBIT 4.6 Greeks for Disney 35 and 37.50 calls.
35 Call37.50 Call
Delta 0.57 0.185
Gamma0.1660.119
Theta −0.013−0.007
Vega 0.0480.032
Rho 0.0230.007
This table compares the ATM call with the OTM call. Kim can reduce her
theta to half that of the ATM call position by purchasing an OTM. This is
certainly a favorable difference. Her vega is lower with the 37.50 call, too.
This may or may not be a favorable difference. That depends on Kim’s
opinion of IV.
On the surface, the disparity in delta appears to be a highly unfavorable
trade-off. The delta of the 37.50 call is less than one third of the delta of the
35 call, and the whole motive for entering into this trade is to trade
direction! Although this strategy is very delta oriented, its core is more
focused on gamma and theta.
The gamma of the 37.50 call is about 72 percent that of the 35 call. But
the theta of the 37.50 call is about half that of the 35 call. Kim is improving
her gamma/theta relationship by buying the OTM, but with the call being so
far out-of-the-money and so inexpensive, the theta needs to be taken with a
grain of salt. It is ultimately gamma that will make or break this delta play.
The price of the option is 0.20—a rather low premium. In order for the
call to gain in value, delta has to go to work with help from gamma. At this
point, the delta is small, only 0.185. If Kim’s forecast is correct and there is
a big move upward, gamma will cause the delta to increase, and therefore
also the premium to increase exponentially. The call’s sensitivity to gamma,
however, is dynamic.
Exhibit 4.7 shows how the gamma of the 37.50 call changes as the stock
price moves over time. At any point in time, gamma is highest when the call
is ATM. However, so is theta. Kim wants to reap as much benefit from
gamma as possible while minimizing her exposure to theta. Ideally, she
wants Disney to rally through the strike price—through the high gamma
and back to the low theta. After three weeks pass, with 23 days until
expiration, if Disney is at $37 a share, the gamma almost doubles, to 0.237.
When the call is ATM, the delta increases at its fastest rate. As Disney rises
above the strike, the gamma figures in the table begin to decline.
EXHIBIT 4.7 Disney 37.50 call price–time matrix–gamma.

Gamma helps as the stock price declines, too. Exhibit 4.8 shows the effect
of time and gamma on the delta of the 37.50 call.
EXHIBIT 4.8 Disney 37.50 call price–time matrix–delta.
The effect of gamma is readily observable, as the delta at any point in
time is always higher at higher stock prices and lower at lower stock prices.
Kim benefits greatly when the delta grows from its initial level of 0.185 to
above 0.50—above the point of being at-the-money. If the stock moves
lower, gamma helps take away the pain of the price decline by decreasing
the delta.
While delta, gamma, and theta occupy Kim’s thoughts, it is ultimately
dollars and cents that matter. She needs to translate her study of the greeks
into cold, hard cash. Exhibit 4.9 shows the theoretical values of the 37.50
call.
EXHIBIT 4.9 Disney 37.50 call price–time matrix–value.
The sooner the price rise occurs, the better. It means less time for theta to
eat away profits. If Kim must hold the position for the entire three weeks,
she needs a good pop in the stock to make it worth her while. At a $37 share
price, the call is worth about 0.50, assuming all other market influences
remain constant. That’s about a 150 percent profit. At $38, Exhibit 4.9
reveals the call value to be 1.04. That’s a 420 percent profit.
On one hand, it’s hard for a trader like Kim not to get excited about the
prospect of making 420 percent on an 8 percent move in a stock. On the
other hand, Kim has to put things in perspective. When the position is
established, the call has a 0.185 delta. By the trader’s definition of delta,
that means the call is estimated to have about an 18.5 percent chance of
expiring in-the-money. More than four out of five times, this position will
be trading below the strike at expiration.
Although Kim is not likely to hold the position until expiration, this
observation tells her something: she’s starting in the hole. She is more likely
to lose than to win. She needs to be compensated well for her risk on the
winners to make up for the more prevalent losers.
Buying OTM calls can be considered more speculative than buying ITM
or ATM calls. Unlike what the at-expiration diagrams would lead one to
believe, OTM calls are not simply about direction. There’s a bit more to it.
They are really about gamma, time, and the magnitude of the stock’s move
(volatility). Long OTM calls require a big move in the right direction for
gamma to do its job.
Long ITM Call
Kim also has the alternative to buy an ITM call. Instead of the 35 or 37.50
call, she can buy the 32.50. The 32.50 call shares some of the advantages
the 37.50 call has over the 35 call, but its overall greek characteristics make
it a very different trade from the two previous alternatives. Exhibit 4.10
shows a comparison of the gr


move in the right direction for
gamma to do its job.
Long ITM Call
Kim also has the alternative to buy an ITM call. Instead of the 35 or 37.50
call, she can buy the 32.50. The 32.50 call shares some of the advantages
the 37.50 call has over the 35 call, but its overall greek characteristics make
it a very different trade from the two previous alternatives. Exhibit 4.10
shows a comparison of the greeks of the three different calls.
EXHIBIT 4.10 Greeks for Disney 32.50, 35, and 37.50 calls.
Like the 37.50 call, the 32.50 has a lower gamma, theta, and vega than the
ATM 35-strike call. Because the call is ITM, it has a higher delta: 0.862. In
this example, Kim can buy the 32.50 call for 3. That’s 0.40 over parity (3 −
[35.10 − 32.50] = 0.40). There is not much time value, but more than the
37.50 call has. Thus, theta is of some concern. Ultimately, the ITMs have
0.40 of time value to lose compared with the 0.20 of the OTM calls. Vega is
also of some concern, but not as much as in the other alternatives because
the vega of the 32.50 is lower than the 35s or the 37.50s. Gamma doesn’t
help much as the stock rallies—it will get smaller as the stock price rises.
Gamma will, however, slow losses somewhat if the stock declines by
decreasing delta at an increasing rate.
In this case, the greek of greatest consequence is delta—it is a more
purely directional play than the other alternatives discussed. Exhibit 4.11
shows the matrix of the delta of the 32.50 call.
EXHIBIT 4.11 Disney 32.50 call price–time matrix–delta.
Because the call starts in-the-money and has a relatively low gamma, the
delta remains high even if Disney declines significantly. Gamma doesn’t
really kick in until the stock retreats enough to bring the call closer to being
at-the-money. At that point, the position will have suffered a big loss, and
the higher gamma is of little comfort.
Kim’s motivation for selecting the ITM call above the ATM and OTM
calls would be increased delta exposure. The 0.86 delta makes direction the
most important concern right out of the gate. Exhibit 4.12 shows the
theoretical values of the 32.50 call.
EXHIBIT 4.12 Disney 32.50 call price–time matrix–value.
Small directional moves contribute to significant leveraged gains or
losses. From share price $35 to $36, the call gains 0.90—from 2.91 to 3.81
—about a 30 percent gain. However, from $35 to $34, the call loses 0.80, or
27 percent. With only 0.40 of time value, the nondirectional greeks (theta,
gamma, and vega) are a secondary consideration.
If this were a deeper ITM call, the delta would start out even higher,
closer to 1.00, and the other relevant greeks would be closer to zero. The
deeper ITM a call, the more it acts like the stock and the less its option
characteristics (greeks) come into play.
Long ATM Put
The beauty of the free market is that two people can study all the available
information on the same stock and come up with completely different
outlooks. First of all, this provides for entertaining television on the
business-news channels when the network juxtaposes an outspoken bullish
analyst with an equally unreserved bearish analyst. But differing opinions
also make for a robust marketplace. Differing opinions are the oil that
greases the machine that is price discovery. From a market standpoint, it’s
what makes the world go round.
It is possible that there is another trader, Mick, in the market studying
Disney, who arrives at the conclusion that the stock is overpriced. Mick
believes the stock will decline in price over the next three weeks. He
decides to buy one Disney March 35 put at 0.80. In this example, March has
44 days to expiration.
Mick initiates this long put position to gain downside exposure, but along
with his bearish position comes option-specific risk and opportunity. Mick
is buying the same month and strike option as Kim did in the first example
of this chapter: the March 35 strike. Despite the different directional bias,
Mick’s position and Kim’s position share many similarities. Exhibit 4.13
offers a comparison of the greeks of the Disney March 35 call and the
Disney March 35 put.
EXHIBIT 4.13 Greeks for Disney 35 call and 35 put.
Call Put
Delta 0.57 −0.444
Gamma0.1660.174
Theta −0.013−0.009
Vega 0.0480.048
Rho 0.023−0.015
The first comparison to note is the contrasting deltas. The put delta is
negative, in contrast to the call delta. The absolute value of the put delta is
close to 1.00 minus the call delta. The put is just slightly OTM, so its delta
is just under 0.50, while that of the call is just over 0.50. The disparate, yet
related deltas represent the main difference between these two trades.
The difference between the gamma of the 35 put and that of the
corresponding call is fairly negligible: 0.174 versus 0.166, respectively. The
gamma of this ATM put will enter into the equation in much the same way
as the gamma of the ATM call. The put’s negative delta will become more
negative as the stock declines, drawing closer to −1.00. It will get less
negative as the stock price rises, drawing closer to zero. Gamma is
important here, because it helps the delta. Delta, however, still remains the
most important greek. Exhibit 4.14 illustrates how the 35 put delta changes
as time and price change.
EXHIBIT 4.14 Disney 35 put price–time matrix–delta.
Since this put is ATM, it starts out with a big enough delta to offer the
directional exposure Mick desires. The delta can change, but gamma
ensures that it always changes in Mick’s favor. Exhibit 4.15 shows how the
value of the 35 put changes with the stock price.
EXHIBIT 4.15 Disney 35 put price–time matrix–value.
Over time, a decline of only 10 percent in the stock yields high
percentage returns. This is due to the leveraged directional nature of this
trade—delta.
While the other greeks are not of primary concern, they must be
monitored. At the onset, the 0.80 premium is all time value and, therefore
subject to the influences of time decay and volatility. This is where trading


put price–time matrix–value.
Over time, a decline of only 10 percent in the stock yields high
percentage returns. This is due to the leveraged directional nature of this
trade—delta.
While the other greeks are not of primary concern, they must be
monitored. At the onset, the 0.80 premium is all time value and, therefore
subject to the influences of time decay and volatility. This is where trading
greeks comes into play.
Conventional trading wisdom says, “Cut your losses early, and let your
profits run.” When trading a stock, that advice is intellectually easy to
understand, although psychologically difficult to follow. Buyers of options,
especially ATM options, must follow this advice from the standpoint of
theta. Options are decaying assets. The time premium will be zero at
expiration. ATMs decay at an increasing nonlinear rate. Exiting a long
position before getting too close to expiration can cut losses caused by an
increasing theta. When to cut those losses, however, will differ from trade
to trade, situation to situation, and person to person.
When buying options, accepting some loss of premium due to time decay
should be part of the trader’s plan. It comes with the territory. In this
example, Mick is willing to accept about three weeks of erosion. Mick
needs to think about what his put will be worth, not just if the underlying
rises or falls but also if it doesn’t move at all. At the time the position is
established, the theta is 0.009, just under a penny. If Disney share price is
unchanged when three weeks pass, his theta will be higher. Exhibit 4.16
shows how thetas and theoretical values change over time if DIS stock
remains at $35.10.
EXHIBIT 4.16 Disney 35 put—thetas and theoretical values.
Mick needs to be concerned not only about what the theta is now but what
it will be when he plans on exiting the position. His plan is to exit the trade
in about three weeks, at which point the put theta will be −0.013. If he
amortizes his theta over this three-week period, he theoretically loses an
average of about 0.01 a day during this time if nothing else changes. The
average daily theta is calculated here by subtracting the value of the put at
23 days to expiration from its value when the trade was established to find
the loss of premium attributed to time decay, then dividing by the number
of days until expiration.
Since the theta doesn’t change much over the first three weeks, Mick can
eyeball the theta rather easily. As expiration approaches and theta begins to
grow more quickly, he’ll need to do the math.
At nine days to expiration, the theoretical value of Mick’s put is about
0.35, assuming all other variables are held constant. By that time, he will
have lost 0.45 (0.80 − 0.35) due to erosion over the 35-day period he held
the position if the stock hasn’t moved. Mick’s average daily theta during
that period is about 0.0129 (0.45 ÷ 35). The more time he holds the trade,
the greater a concern is theta. Mick must weigh his assessment of the
likelihood of the option’s gaining value from delta against the risk of
erosion. If he holds the trade for 35 days, he must make 0.0129 on average
per day from delta to offset theta losses. If the forecast is not realized within
the expected time frame or if the forecast changes, Mick needs to act fast to
curtail average daily theta losses.
Finding the Right Risk
Mick could lower the theta of his position by selecting a put with a greater
number of days to expiration. This alternative has its own set of trade-offs:
lower gamma and higher vega than the 44-day put. He could also select an
ITM put or an OTM put. Like Kim’s call alternatives, the OTM put would
have less exposure to time decay, lower vega, lower gamma, and a lower
delta. It would have a lower premium, too. It would require a bigger price
decline than the ATM put and would be more speculative.
The ITM put would also have lower theta, vega, and gamma, but it would
have a higher delta. It would take on more of the functionality of a short
stock position in much the same way that Kim’s ITM call alternative did for
a long stock position. In its very essence, however, an option trade, ITM or
otherwise, is still fundamentally different than a stock trade.
Stock has a 1.00 delta. The delta of a stock never changes, so it has zero
gamma. Stock is not subject to time decay and has no volatility component
to its pricing. Even though ITM options have deltas that approach 1.00 and
other greeks that are relatively low, they have two important differences
from an equity. The first is that the greeks of options are dynamic. The
second is the built-in leverage feature of options.
The relationship of an option’s strike price to the stock price can change
constantly. Options that are ITM now may be OTM tomorrow and vice
versa. Greeks that are not in play at the moment may be later. Even if there
is no time value in the option now because it is so far away-from-the-
money, there is the potential for time premium to become a component of
the option’s price if the stock moves closer to the strike price. Gamma,
theta, and vega always have the potential to come into play.
Since options are leveraged by nature, small moves in the stock can
provide big profits or big losses. Options can also curtail big losses if used
for hedging. Long option positions can reap triple-digit percentage gains
quickly with a favorable move in the underlying. Even though 100 percent
of the premium can be lost just as easily, one option contract will have far
less nominal exposure than a similar position in the stock.
It’s All About Volatility
What are Kim and Mick really trading? Volatility. The motivation for
buying an option as opposed to buying or shorting the stock is volatility. To
some degree, these options have exposure to both flavors of volatility—
implied volatility and historical volatility (HV). The positions in each of the
examples have positive vega. Their values are influenced, in part, by IV.
Over time, IV begins


ility
What are Kim and Mick really trading? Volatility. The motivation for
buying an option as opposed to buying or shorting the stock is volatility. To
some degree, these options have exposure to both flavors of volatility—
implied volatility and historical volatility (HV). The positions in each of the
examples have positive vega. Their values are influenced, in part, by IV.
Over time, IV begins to lose its significance if the option is no longer close
to being at-the-money.
The main objective of each of these trades is to profit from the volatility
of the stock’s price movement, called future stock volatility or future
realized volatility. The strategies discussed in this chapter are contingent on
volatility being one directional. The bigger the move in the trader’s
forecasted direction the better. Volatility in the form of an adverse
directional move results in a decline in premium. The gamma in these long
option positions makes volatility in the right direction more beneficial and
volatility in the wrong direction less costly.
This phenomenon is hardly unique to the long call and the long put.
Although some basic strategies, such as the ones studied in this chapter,
depend on a particular direction, many don’t. Except for interest rate
strategies and perhaps some arbitrage strategies, all option trades are
volatility trades in one way or another. In general, option strategies can be
divided into two groups: volatility-buying strategies and volatility-selling
strategies. The following is a breakdown of common option strategies into
categories of volatility-buying strategies and volatility-selling strategies:
Volatility-Selling Strategies Volatility-Buying Strategies
Short Call, Short Put, Covered Call, Covered Put,
Bull Call Spread, Bear Call Spread, Bull Put
Spread, Bear Put Spread, Short Straddle, Short
Strangle, Guts, Ratio Call Spread, Calendar,
Butterfly, Iron Butterfly, Broken-Wing Butterfly,
Condor, Iron Condor, Diagonals, Double Diagonals,
Risk Reversals/Collars.
Long Call, Long Put, Bull Call Spread, Bear
Call Spread, Bull Put Spread, Bear Put Spread,
Long Straddle, Long Strangle, Guts, Back
Spread, Calendar, Butterfly, Iron Butterfly,
Broken-Wing Butterfly, Condor, Iron Condor,
Diagonals, Double Diagonals, Risk
Reversals/Collars.
Long option strategies appear in the volatility-buying group because they
have positive gamma and positive vega. Short option strategies appear in
the volatility-selling group because of negative gamma and vega. There are
some strategies that appear in both groups—for example, the
butterfly/condor family, which is typically associated with income
generation. These particular volatility strategies are commonly instituted as
volatility-selling strategies. However, depending on whether the position is
bought or sold and where the stock price is in relation to the strike prices,
the position could fall into either group. Some strategies, like the vertical
spread family—bull and bear call and put spreads—and risk reversal/collar
spreads naturally fall into either category, depending on where the stock is
in relation to the strikes. The calendar spread family is unique in that it can
have characteristics of each group at the same time.
Direction Neutral, Direction Biased, and
Direction Indifferent
As typically traded, volatility-selling option strategies are direction neutral.
This means that the position has the greatest results if the underlying price
remains in a range—that is, neutral. Although some option-selling strategies
—for example, a naked put—may have a positive or negative delta in the
short term, profit potential is decidedly limited. This means that if traders
are expecting a big move, they are typically better off with option-buying
strategies.
Option-buying strategies can be either direction biased or direction
indifferent. Direction-biased strategies have been shown throughout this
chapter. They are delta trades. Direction-indifferent strategies are those that
benefit from increased volatility in the underlying but where the direction of
the move is irrelevant to the profitability of the trade. Movement in either
direction creates a winner.
Are You a Buyer or a Seller?
The question is: which is better, selling volatility or buying volatility? I
have attended option seminars with instructors (many of whom I regard
with great respect) teaching that volatility-selling strategies, or income-
generating strategies, are superior to buying options. I also know option
gurus that tout the superiority of buying options. The answer to the question
of which is better is simple: it’s all a matter of personal preference.
When I began trading on the floor of Chicago Board Options Exchange
(CBOE) in the 1990s, I quickly became aware of a dichotomy among my
market-making peers. Those making markets on the floor of the exchange at
that time were divided into two groups: teenie buyers and teenie sellers.
Teenie Buyers
Before options traded in decimals (dollars and cents) like they do today, the
lowest price increment in which an option could be traded was one
sixteenth of a dollar—a teenie . Teenie buyers were market makers who
would buy back OTM options at one sixteenth to eliminate short positions.
They would sometimes even initiate long OTM option positions at a teenie,
too. The focus of the teenie-buyer school of thought was the fact that long
options have unlimited reward, while short options have unlimited risk. An
option purchased so far OTM that it was offered at one sixteenth is unlikely
to end up profitable, but it’s an inexpensive lottery ticket. At worst, the
trader can only lose a teenie. Teenie buyers felt being short OTM options
that could be closed by paying a sixteenth was an unreasonable risk.
Teenie Sellers
Teenie sellers, however, focused on the fact that options offered at one
sixteenth were far enough OTM that they were very likely to expire
worthless. This appears to be free money, unless the unexpected occurs, in
which case potentia


st, the
trader can only lose a teenie. Teenie buyers felt being short OTM options
that could be closed by paying a sixteenth was an unreasonable risk.
Teenie Sellers
Teenie sellers, however, focused on the fact that options offered at one
sixteenth were far enough OTM that they were very likely to expire
worthless. This appears to be free money, unless the unexpected occurs, in
which case potential losses can be unlimited. Teenie sellers would routinely
save themselves $6.25 (one sixteenth of a dollar per contract representing
100 shares) by selling their long OTMs at a teenie to close the position.
They sometimes would even initiate short OTM contracts at one sixteenth.
These long-option or short-option biases hold for other types of strategies
as well. Volatility-selling positions, such as the iron condor, can be
constructed to have limited risk. The paradigm for these strategies is they
tend to produce winners more often than not. But when the position loses,
the trader loses more than he would stand to profit if the trade worked out
favorably.
Herein lies the issue of preference. Long-option traders would rather trade
Babe Ruth–style. For years, Babe Ruth was the record holder for the most
home runs. At the same time, he was also the record holder for the most
strikeouts. The born fighters that are option buyers accept the fact that they
will have more strikeouts, possibly many more strikeouts, than winning
trades. But the strategy dictates that the profit on one winner more than
makes up for the string of small losers.
Short-option traders, conversely, like to have everything cool and
copacetic. They like the warm and fuzzy feeling they get from the fact that
month after month they tend to generate winners. The occasional loser that
nullifies a few months of profits is all part of the game.
Options and the Fair Game
There may be a statistical advantage to buying stock as opposed to shorting
stock, because the market has historically had a positive annualized return
over the long run. A statistical advantage to being either an option buyer or
an option seller, however, should not exist in the long run, because the
option market prices IV. Assuming an overall efficient market for pricing
volatility into options, there should be no statistical advantage to
systematically buying or selling options. 1
Consider a game consisting of one six-sided die. Each time a one, two, or
three is rolled, the house pays the player $1. Each time a four, five, or six is
rolled, the house pays zero. What is the most a player would be willing to
pay to play this game? If the player paid nothing, the house would be at a
tremendous disadvantage, paying $1 50 percent of the time and nothing the
other 50 percent of the time. This would not be a fair game from the house’s
perspective, as it would collect no money. If the player paid $1, the player
would get his dollar back when one, two, or three came up. Otherwise, he
would lose his dollar. This is not a fair game from the player’s perspective.
The chances of winning this game are 3 out of 6, or 50–50. If this game
were played thousands of times, one would expect to receive $1 half the
time and receive nothing the other half of the time. The average return per
roll one would expect to receive would be $0.50, that’s ($1 × 50 percent +
$0 × 50 percent). This becomes a fair game with an entrance fee of $0.50.
Now imagine a similar game in which a six-sided die is rolled. This time
if a one is rolled, the house pays $1. If any other number is rolled, the house
pays nothing. What is a fair price to play this game? The same logic and the
same math apply. There is a
 percent chance of a one coming up and the
player receiving $1. And there is a
 percent chance of each of the other
five numbers being rolled and the player receiving nothing. Mathematically,
this translates to:
 percent
 percent). Fair value for a
chance to play this game is about $0.1667 per roll.
The fair game concept applies to option prices as well. The price of the
game, or in this case the price of the option, is determined by the market in
the form of IV. The odds are based on the market’s expectations of future
volatility. If buying options offered a superior payout based on the odds of
success, the market would put upward pressure on prices until this arbitrage
opportunity ceased to exist. It’s the same for selling volatility. If selling
were a fundamentally better strategy, the market would depress option
prices until selling options no longer produced a way to beat the odds. The
options market will always equalize imbalances.
Note
1 . This is not to say that unique individual opportunities do not exist for
overpriced or underpriced options, only that options are not overpriced or
underpriced in general. Thus, neither an option-selling nor option-buying
methodology should provide an advantage.
CHAPTER 5
An Introduction to Volatility-Selling Strategies
Along with death and taxes, there is one other fact of life we can all count
on: the time value of all options ultimately going to zero. What an alluring
concept! In a business where expected profits can be thwarted by an
unexpected turn of events, this is one certainty traders can count on. Like all
certainties in the financial world, there is a way to profit from this fact, but
it’s not as easy as it sounds. Alas, the potential for profit only exists when
there is risk of loss.
In order to profit from eroding option premiums, traders must implement
option-selling strategies, also known as volatility-selling strategies. These
strategies have their own set of inherent risks. Selling volatility means
having negative vega—the risk of implied volatility rising. It also means
having negative gamma—the risk of the underlying being too volatile. This
is the nature of selling volatility. The option-selling trader does not want the
underlying stock to move—that is, the trader wants the stock to be less
volatile. That is the risk.
Profit Potential
Prof


n set of inherent risks. Selling volatility means
having negative vega—the risk of implied volatility rising. It also means
having negative gamma—the risk of the underlying being too volatile. This
is the nature of selling volatility. The option-selling trader does not want the
underlying stock to move—that is, the trader wants the stock to be less
volatile. That is the risk.
Profit Potential
Profit for the volatility seller is realized in a roundabout sort of way. The
reward for low volatility is achieved through time decay. These strategies
have positive theta. Just as the volatility-buying strategies covered in
Chapter 4 had time working against them, volatility-selling strategies have
time working in their favor. The trader is effectively paid to assume the risk
of movement.
Gamma-Theta Relationship
There exists a trade-off between gamma and theta. Long options have
positive gamma and negative theta. Short options have negative gamma and
positive theta. Positions with greater gamma, whether positive or negative,
tend to have greater theta values, negative or positive. Likewise, lower
absolute values for gamma tend to go hand in hand with lower absolute
values for theta. The gamma-theta relationship is the most important
consideration with many types of strategies. Gamma-theta is often the
measurement with the greatest influence on the bottom line.
Greeks and Income Generation
With volatility-selling strategies (sometimes called income-generating
strategies), greeks are often overlooked. Traders simply dismiss greeks as
unimportant to this kind of trade. There is some logic behind this reasoning.
Time decay provides the profit opportunity. In order to let all of time
premium erode, the position must be held until expiration. Interim changes
in implied volatility are irrelevant if the position is held to term. The
gamma-theta loses some significance if the position is held until expiration,
too. The position has either passed the break-even point on the at-expiration
diagram, or it has not. Incremental daily time decay–related gains are not
the ultimate goal. The trader is looking for all the time premium, not
portions of it.
So why do greeks matter to volatility sellers? Greeks allow traders to be
flexible. Consider short-term-momentum stock traders. The traders buy a
stock because they believe it will rise over the next month. After one week,
if unexpected bearish news is announced causing the stock to break through
its support lines, the traders have a decision to make. Short-term speculative
traders very often choose to cut their losses and exit the position early rather
than risk a larger loss hoping for a recovery.
Volatility-selling option traders are often faced with the same dilemma. If
the underlying stays in line with the traders’ forecast, there is little to worry
about. But if the environment changes, the traders have to react. Knowing
the greeks for a position can help traders make better decisions if they plan
to close the position before expiration.
Naked Call
A naked call is when a trader shorts a call without having stock or other
options to cover or protect it. Since the call is uncovered, it is one of the
riskier trades a trader can make. Recall the at-expiration diagram for the
naked call from Chapter 1, Exhibit 1.3 : Naked TGT Call. Theoretically,
there is limited reward and unlimited risk. Yet there are times when
experienced traders will justify making such a trade. When a stock has been
trading in a range and is expected to continue doing so, traders may wait
until it is near the top of the channel, where there is resistance, and then
short a call.
For example, a trader, Brendan, has been studying a chart of Johnson &
Johnson (JNJ). Brendan notices that for a few months the stock has trading
been in a channel between $60 and $65. As he observes Johnson & Johnson
beginning to approach the resistance level of $65 again, he considers selling
a call to speculate on the stock not rising above $65. Before selling the call,
Brendan consults other technical analysis tools, like ADX/DMI, to confirm
that there is no trend present. ADX/DMI is used by some traders as a filter
to determine the strength of a trend and whether the stock is overbought or
oversold. In this case, the indicator shows no strong trend present. Brendan
then performs due diligence. He studies the news. He looks for anything
specific that could cause the stock to rally. Is the stock a takeover target?
Brendan finds nothing. He then does earnings research to find out when
they will be announced, which is not for almost two more months.
Next, Brendan pulls up an option chain on his computer. He finds that
with the stock trading around $64 per share, the market for the November
65 call (expiring in four weeks) is 0.66 bid at 0.68 offer. Brendan considers
when Johnson & Johnson’s earnings report falls. Although recent earnings
have seldom been a major concern for Johnson & Johnson, he certainly
wants to sell an option expiring before the next earnings report. The
November fits the mold. Brendan sells ten of the November 65 calls at the
bid price of 0.66.
Brendan has a rather straightforward goal. He hopes to see Johnson &
Johnson shares remain below $65 between now and expiration. If he is
right, he stands to make $660. If he is wrong? Exhibit 5.1 shows how
Brendan’s calls hold up if they are held until expiration.
EXHIBIT 5.1 Naked Johnson & Johnson call at expiration.
Considering the risk/reward of this trade, Brendan is rightfully concerned
about a big upward move. If the stock begins to rally, he must be prepared
to act fast. Brendan must have an idea in advance of what his pain threshold
is. In other words, at what price will he buy back his calls and take a loss if
Johnson & Johnson moves adversely?
He decides he will buy all 10 of his calls back at 1.10 per contract if the
trade goes against him. (1.10 is an arbitrary price used for illustrative
purposes. The actual price will vary, based on the si


ared
to act fast. Brendan must have an idea in advance of what his pain threshold
is. In other words, at what price will he buy back his calls and take a loss if
Johnson & Johnson moves adversely?
He decides he will buy all 10 of his calls back at 1.10 per contract if the
trade goes against him. (1.10 is an arbitrary price used for illustrative
purposes. The actual price will vary, based on the situation and the risk
tolerance of the trader. More on when to take profits and losses is discussed
in future chapters.) He may choose to enter a good-till-canceled (GTC)
stop-loss order to buy back his calls. Or he may choose to monitor the stock
and enter the order when he sees the calls offered at 1.10—a mental stop
order. What Brendan needs to know is: How far can the stock price advance
before the calls are at 1.10?
Brendan needs to examine the greeks of this trade to help answer this
question. Exhibit 5.2 shows the hypothetical greeks for the position in this
example.
EXHIBIT 5.2 Greeks for short Johnson & Johnson 65 call (per contract).
Delta −0.34
Gamma−0.15
Theta 0.02
Vega −0.07
The short call has a negative delta. It also has negative gamma and vega,
but it has positive time decay (theta). As Johnson & Johnson ticks higher,
the delta increases the nominal value of the call. Although this is not a
directional trade per se, delta is a crucial element. It will have a big impact
on Brendan’s expectations as to how high the stock can rise before he must
take his loss.
First, Brendan considers how much the option price can move before he
covers. The market now is 0.66 bid at 0.68 offer. To buy back his calls at
1.10, they must be offered at 1.10. The difference between the offer now
and the offer price at which Brendan will cover is 0.42 (that’s 1.10 − 0.68).
Brendan can use delta to convert the change in the ask prices into a stock
price change. To do so, Brendan divides the change in the option price by
the delta.
The −0.34 delta indicates that if JNJ rises $1.24, the calls should be
offered at 1.10.
Brendan takes note that the bid-ask spreads are typically 0.01 to 0.03
wide in near-term Johnson & Johnson options trading under 1.00. This is
not necessarily the case in other option classes. Less liquid names have
wider spreads. If the spreads were wider, Brendan would have more
slippage. Slippage is the difference between the assumed trade price and the
actual price of the fill as a product of the bid-ask spread. It’s the difference
between theory and reality. If the bid-ask spread had a typical width of, say,
0.70, the market would be something more like 0.40 bid at 1.10 offer. In
this case, if the stock moved even a few cents higher, Brendan could not
buy his calls back at his targeted exit price of 1.10. The tighter markets
provide lower transaction costs in the form of lower slippage. Therefore,
there is more leeway if the stock moves adversely when there are tighter
bid-ask option spreads.
But just looking at delta only tells a part of the story. In reality, the delta
does not remain constant during the price rise in Johnson & Johnson but
instead becomes more negative. Initially, the delta is −0.34 and the gamma
is −0.15. After a rise in the stock price, the delta will be more negative by
the amount of the gamma. To account for the entire effect of direction,
Brendan needs to take both delta and gamma into account. He needs to
estimate the average delta based on gamma during the stock price move.
The formula for the change in stock price is
Taking into account the effect of gamma as well as delta, Johnson &
Johnson needs to rise only $1.01, in order for Brendan’s calls to be offered
at his stop-loss price of 1.10.
While having a predefined price point to cover in the event the underlying
rises is important, sometimes traders need to think on their feet. If material
news is announced that changes the fundamental outlook for the stock,
Brendan will have to adjust his plan. If the news leads Brendan to become
bullish on the stock, he should exit the trade at once, taking a small loss
now instead of the bigger loss he would expect later. If the trader is
uncertain as to whether to hold or close the position, the Would I Do It
Now? rule is a useful rule of thumb.
Would I Do It Now? Rule
To follow this rule, ask yourself, “If I did not already have this position,
would I do it now? Would I establish the position at the current market
prices, given the current market scenario?” If the answer is no, then the
solution is simple: Exit the trade.
For example, if after one week material news is released and Johnson &
Johnson is trading higher, at $64.50 per share, and the November 65 call is
trading at 0.75, Brendan must ask himself, based on the price of the stock
and all known information, “If I were not already short the calls, would I
short them now at the current price of 0.75, with the stock trading at
$64.50?”
Brendan’s opinion of the stock is paramount in this decision. If, for
example, based on the news that was announced he is now bullish, he
would likely not want to sell the calls at 0.75—he only gets $0.09 more in
option premium and the stock is 0.50 closer to the strike. If, however, he is
not bullish, there is more to consider.
Theta can be of great use in decision making in this situation. As the
number of days until expiration decreases and the stock approaches $65
(making the option more at-the-money), Brendan’s theta grows more
positive. Exhibit 5.3 shows the theta of this trade as the underlying rises
over time.
EXHIBIT 5.3 Theta of Johnson & Johnson.
When the position is first established, positive theta comforts Brendan by
showing that with each passing day he gets a little closer to his goal—to
have the 65 calls expire out-of-the-money (OTM) and reap a profit of the
entire 66-cent premium. Theta becomes truly useful if the position begins to
move against him. As Johnson & Johnson rises, the trade gets more
precarious. His negative delta increases. His negative gamma increases.


ed, positive theta comforts Brendan by
showing that with each passing day he gets a little closer to his goal—to
have the 65 calls expire out-of-the-money (OTM) and reap a profit of the
entire 66-cent premium. Theta becomes truly useful if the position begins to
move against him. As Johnson & Johnson rises, the trade gets more
precarious. His negative delta increases. His negative gamma increases. His
goal becomes more out of reach. In conjunction with delta and gamma,
theta helps Brendan decide whether the risk is worth the reward.
In the new scenario, with the stock at $64.50, Brendan would collect $18
a day (1.80 × 10 contracts). Is the risk of loss in the short run worth earning
$18 a day? With Johnson & Johnson at $64.50, would Brendan now short
10 calls at 0.75 to collect $18 a day, knowing that each day may bring a
continued move higher in the stock? The answer to this question depends on
Brendan’s assessment of the risk of the underlying continuing its ascent. As
time passes, if the stock remains closer to the strike, the daily theta rises,
providing more reward. Brendan must consider that as theta—the reward—
rises, so does gamma: a risk factor.
A small but noteworthy risk is that implied volatility could rise. The
negative vega of this position would, then, adversely affect the profitability
of this trade. It will make Brendan’s 1.10 cover-point approach faster
because it makes the option more expensive. Vega is likely to be of less
consequence because it would ultimately take the stock’s rising though the
strike price for the trade to be a loser at expiration.
Short Naked Puts
Another trader, Stacie, has also been studying Johnson & Johnson. Stacie
believes Johnson & Johnson is on its way to test the $65 resistance level yet
again. She believes it may even break through $65 this time, based on
strong fundamentals. Stacie decides to sell naked puts. A naked put is a
short put that is not sold in conjunction with stock or another option.
With the stock around $64, the market for the November 65 put is 1.75
bid at 1.80. Stacie likes the fact that the 65 puts are slightly in-the-money
(ITM) and thus have a higher delta. If her price rise comes sooner than
expected, the high delta may allow her to take a profit early. Stacie sells 10
puts at 1.75.
In the best-case scenario, Stacie retains the entire 1.75. For that to happen,
she will need to hold this position until expiration and the stock will have to
rise to be trading above the 65 strike. Logically, Stacie will want to do an
at-expiration analysis. Exhibit 5.4 shows Stacie’s naked put trade if she
holds it until expiration.
EXHIBIT 5.4 Naked Johnson & Johnson put at expiration.
While harvesting the entire premium as a profit sounds attractive, if
Stacie can take the bulk of her profit early, she’ll be happy to close the
position and eliminate her risk—nobody ever went broke taking a profit.
Furthermore, she realizes that her outlook may be wrong: Johnson &
Johnson may decline. She may have to close the position early—maybe for
a profit, maybe for a loss. Stacie also needs to study her greeks. Exhibit 5.5
shows the greeks for this trade.
EXHIBIT 5.5 Greeks for short Johnson & Johnson 65 put (per contract).
Delta 0.65
Gamma−0.15
Theta 0.02
Vega −0.07
The first item to note is the delta. This position has a directional bias. This
bias can work for or against her. With a positive 0.65 delta per contract, this
position has a directional sensitivity equivalent to being long around 650
shares of the stock. That’s the delta × 100 shares × 10 contracts.
Stacie’s trade is not just a bullish version of Brendan’s. Partly because of
the size of the delta, it’s different—specific directional bias aside. First, she
will handle her trade differently if it is profitable.
For example, if over the next week or so Johnson & Johnson rises $1,
positive delta and negative gamma will have a net favorable effect on
Stacie’s profitability. Theta is small in comparison and won’t have too much
of an effect. Delta/gamma will account for a decrease in the put’s
theoretical value of about $0.73. That’s the estimated average delta times
the stock move, or [0.65 + (–0.15/2)] × 1.00.
Stacie’s actual profit would likely be less than 0.73 because of the bid-ask
spread. Stacie must account for the fact that the bid-ask is 0.05 wide (1.75–
1.80). Because Stacie would buy to close this position, she should consider
the 0.73 price change relative to the 1.80 offer, not the 1.75 trade price—
that is, she factors in a nickel of slippage. Thus, she calculates, that the puts
will be offered at 1.07 (that’s 1.80 − 0.73) when the stock is at $65. That is
a gain of $0.68.
In this scenario, Stacie should consider the Would I Do It Now? rule to
guide her decision as to whether to take her profit early or hold the position
until expiration. Is she happy being short ten 65 puts at 1.07 with Johnson
& Johnson at $65? The premium is lower now. The anticipated move has
already occurred, and she still has 28 days left in the option that could allow
for the move to reverse itself. If she didn’t have the trade on now, would she
sell ten 65 puts at 1.07 with Johnson & Johnson at $65? Based on her
original intention, unless she believes strongly now that a breakout through
$65 with follow-through momentum is about to take place, she will likely
take the money and run.
Stacie also must handle this trade differently from Brendan in the event
that the trade is a loser. Her trade has a higher delta. An adverse move in the
underlying would affect Stacie’s trade more than it would Brendan’s. If
Johnson & Johnson declines, she must be conscious in advance of where
she will cover.
Stacie considers both how much she is willing to lose and what potential
stock-price action will cause her to change her forecast. She consults a
stock chart of Johnson & Johnson. In this example, we’ll assume there is
some resistance developing around $64 in the short term. If this resistance
level holds, the trade


son & Johnson declines, she must be conscious in advance of where
she will cover.
Stacie considers both how much she is willing to lose and what potential
stock-price action will cause her to change her forecast. She consults a
stock chart of Johnson & Johnson. In this example, we’ll assume there is
some resistance developing around $64 in the short term. If this resistance
level holds, the trade becomes less attractive. The at-expiration breakeven is
$63.25, so the trade can still be a winner if Johnson & Johnson retreats. But
Stacie is looking for the stock to approach $65. She will no longer like the
risk/reward of this trade if it looks like that price rise won’t occur. She
makes the decision that if Johnson & Johnson bounces off the $64 level
over the next couple weeks, she will exit the position for fear that her
outlook is wrong. If Johnson & Johnson drifts above $64, however, she will
ride the trade out.
In this example, Stacie is willing to lose 1.00 per contract. Without taking
into account theta or vega, that 1.00 loss in the option should occur at a
stock price of about $63.28. Theta is somewhat relevant here. It helps
Stacie’s potential for profit as time passes. As time passes and as the stock
rises, so will theta, helping her even more. If the stock moves lower (against
her) theta helps ease the pain somewhat, but the further in-the-money the
put, the lower the theta.
Vega can be important here for two reasons: first, because of how implied
volatility tends to change with market direction, and second, because it can
be read as an indication of the market’s expectations.
The Double Whammy
With the stock around $64, there is a negative vega of about seven cents. As
the stock moves lower, away from the strike, the vega gets a bit smaller.
However, the market conditions that would lead to a decline in the price of
Johnson & Johnson would likely cause implied volatility (IV) to rise. If the
stock drops, Stacie would have two things working against her—delta and
vega—a double whammy. Stacie needs to watch her vega. Exhibit 5.6
shows the vega of Stacie’s put as it changes with time and direction.
EXHIBIT 5.6 Johnson & Johnson 65 put vega.
If after one week passes Johnson & Johnson gaps lower to, say, $63.00 a
share, the vega will be 0.043 per contract. If IV subsequently rises 5 points
as a result of the stock falling, vega will make Stacie’s puts theoretically
worth 21.5 cents more per contract. She will lose $215 on vega (that’s 0.043
vega × 5 volatility points × 10 contracts) plus the adverse delta/gamma
move.
A gap opening will cause her to miss the opportunity to stop herself out at
her target price entirely. Even if the stock drifts lower, her targeted stop-loss
price will likely come sooner than expected, as the option price will likely
increase both by delta/gamma and vega resulting from rising volatility. This
can cause her to have to cover sooner, which leaves less room for error.
With this trade, increases in IV due to market direction can make it feel as if
the delta is greater than it actually is as the market declines. Conversely, IV
softening makes it feel as if the delta is smaller than it is as the market rises.
The second reason IV has importance for this trade (as for most other
strategies) is that it can give some indication of how much the market thinks
the stock can move. If IV is higher than normal, the market perceives there
to be more risk than usual of future volatility. The question remains: Is the
higher premium worth the risk?
The answer to this question is subjective. Part of the answer is based on
Stacie’s assessment of future volatility. Is the market right? The other part is
based on Stacie’s risk tolerance. Is she willing to endure the greater price
swings associated with the potentially higher volatility? This can mean
getting whipsawed, which is exiting a position after reaching a stop-loss
point only to see the market reverse itself. The would-be profitable trade is
closed for a loss. Higher volatility can also mean a higher likelihood of
getting assigned and acquiring an unwanted long stock position.
Cash-Secured Puts
There are some situations where higher implied volatility may be a
beneficial trade-off. What if Stacie’s motivation for shorting puts was
different? What if she would like to own the stock, just not at the current
market price? Stacie can sell ten 65 puts at 1.75 and deposit $63,250 in her
trading account to secure the purchase of 1,000 shares of Johnson &
Johnson if she gets assigned. The $63,250 is the $65 per share she will pay
for the stock if she gets assigned, minus the 1.75 premium she received for
the put × $100 × 10 contracts. Because the cash required to potentially
purchase the stock is secured by cash sitting ready in the account, this is
called a cash-secured put.
Her effective purchase price if assigned is $63.25—the same as her
breakeven at expiration. The idea with this trade is that if Johnson &
Johnson is anywhere under $65 per share at expiration, she will buy the
stock effectively at $63.25. If assigned, the time premium of the put allows
her to buy the stock at a discount compared with where it is priced when the
trade is established, $64. The higher the time premium—or the higher the
implied volatility—the bigger the discount.
This discount, however, is contingent on the stock not moving too much.
If it is above $65 at expiration she won’t get assigned and therefore can
only profit a maximum of 1.75 per contract. If the stock is below $63.25 at
expiration, the time premium no longer represents a discount, in fact, the
trade becomes a loser. In a way, Stacie is still selling volatility.
Covered Call
The problem with selling a naked call is that it has unlimited exposure to
upside risk. Because of this, many traders simply avoid trading naked calls.
A more common, and some would argue safer, method of selling calls is to
sell them covered.
A covered call is when calls are sold and stock is purchased on a sha