An Introduction To Volatility
Before
I begin this lesson I must inform you that I’ve got both good news
and bad news for you, the retail trader/investor, who is attempting to learn
about volatility. So which would you like first, the good news or the bad news?
I always like to begin with the bad news: The bad news is that volatility
is one of the most crucial yet frequently misunderstood concepts in the options
trading game. Moreover ( for the less
quantitatively inclined among you), it is one of the most purely mathematical,
deriving straight from probability theory. The
terms “standard deviation,†“mean
reversion†and “serial
correlation†are each important for an overall understanding of
volatility.
What
about the good news, you say? Well the
good news is that for the retail trader and small investor, mastering the
complexities of volatility is a nicety rather than a necessity. You simply
don’t have to learn all the same nuances of volatility that the professional
trader must. For the retail trader,
various other factors play a much greater role in your trading success — chief
among these being the establishment of your individual threshold for risk;
the adroit selection of stocks; and the timing of price movements and
trends. Nonetheless, every options trader
should have a grasp at least of a few fundamental principals of volatility, and
the outlining of these is my task at hand.
Let’s
cut to the chase. First and foremost, volatility is an essential concept in
determining the value of an option. It
can be looked at from two angles: conceptually
and mathematically. Conceptually,
Volatility is essentially the measurement of a stock’s ( or other
underlying’s) tendency to move up and down in price over a given period of
time. It is also, as we shall see,
the only variable in an option pricing model not known with certainty in
advance. Mathematically,
volatility can be defined as is the annualized
standard deviation of daily returns of a given underlying.
Note that options practitioners always talk about volatility in terms of
percentages. For example, a rise in
“vol.†in stock (or Index) ABC from
100-101 is equal to a rise in stock (or Index)
BCD from 300-303, because
in both cases the changes is equal to 1 percent.
It
is important to know that volatility has a straightforward relationship with the
option’s price: As the percentage of volatility increases, the price of the
option likewise increases. Why is this
so? Follow the logic: First, an
options volatility is tied to the price movement of the underlying instrument.
Second, a higher volatility means that the stock has a greater likelihood
of movement. Third, a stock with a
greater likelihood of movement has a higher probability of reaching the exercise
price. And fourth, a stock with a higher probability of reaching its exercise
price will have a relatively higher price than one with a lower probability of
reaching the exercise price. Mathematically,
all this can be demonstrated mathematically, and graphically by a look at low
medium and high volatility distribution curves. But
you don’t need to get into all of that!
But,
you might ask, what about the difference between puts and calls?
Does volatility affect each differently, such that higher volatility
might increase the value of a call while decreasing the value of a put, or vice
versa? This might make intuitive
sense, but the answer is no.yes”> This movement can be either up or down.If
we examine a chart of the history of a stock’s price movement, we would
discover that each individual stock passes through periods of low volatility and
also periods of high volatility. What
accounts for these fluctuations in price? There
are numerous possibilities. Macro and or
microeconomic factors affecting the particular company could certainly do it.
Also, macroeconomic influences on the company’s sector or industry
could also be a cause. Maybe the
investors of the particular stock heard a rumor– who knows?
The point is the causes for a stocks price fluctuation are myriad.
I
lied. I am going to through a little bit
of math at you, and here it is. Regardless
of the cause, volatility tends to be –Volatility over a given time
period is highly correlated to the volatility of the previous identical time
period. In other words, the volatility of the next 30 days is statistically
likely to be similar o the last 30 days. This
interesting characteristic is referred to as serial
correlation.
Volatility
fluctuates inversely with respect to time. As
short term volatility is moved away from the mean by various and sundry short
term events, it has less chance to return to the mean because of time
restriction. Longer-term volatility, on
the other hand, has a greater amount of time to revert to that mean.
It is important to
note that options practitioners actually describe volatility in four different
ways.
Typically,
volatility is broken down into 4 types:
1.
Historical
Volatility. Historical
volatility is, for the most part, what we have been talking about so far it this
lesson. It is the measure of price
changes of an instrument (a stock, index, etc.) over a given period of time.
Think of it as the instruments “up
and downness,†for a short and cute definition.
And, to repeat, we can get fancy and look at it mathematically as the
stock’s annualized standard deviation of daily returns.
But let’s keep it simple…
2.
Expected
Volatility is a very
subjective creature. This simply refers
to the trader’s best guess as to what
volatility will be. Of course, these aren’t BLIND guesses, most traders study
historical charts and look at market conditions to come up with the expected
volatility value. But they are estimates nonetheless.
3.
Future
Volatility I like to
think, kind of the
mathematician’s way of saying Expected volatility.
By definition it is the Annualized standard deviation of daily returns
during a yet to be specified future period of time.
This period typically extends from the present to the option’s
expiration. But hold on a minute:
for a future period of time? How
can a trader now this value? Well,
he can’t; only historical volatility can be known with certainty, because it
has already happened!
Traders
use sophisticated pricing models to
determine the theoretical value of an
option. Most of these pricing formulae
derive in some way from the Black-Scholes model.
Now these models have a number of variables that must be input in order
for them to spit out the theoretical value.
These variables include Exercise price, Underlying price, Time to
Expiration, Interest Rates, Dividends, and Volatility.
The model plugs all these numbers into a model developed by a rocket
scientist and pops out a theoretical value.
Now look hard: which of the above input-values is not known ahead
of time, and with certainty? You
guessed it : VOLATILITY.
So the volatility values that these sophisticated models use to produce
their vaunted theoretical values are really no more than estimates!
This may come as a shock to some of you that guesswork plays such a role
in pricing models, but it does. To
summarize, Future Volatility is the number needed to plug into an option pricing
model in order to determine an option’s theoretical value.
4.
Implied
Volatility. I
saved the hardest one for last! Implied
Volatility is the volatility value ( remember, expressed in % form) that
justifies or
To understand what the heck this means, let’s go back to our discussion
of the pricing model above. Recall
we said that the trader plugs in various values into his sophisticated pricing
model or formula, including one for Volatility ( the “future Vol. Numberâ€),
and out pops a number called the theoretical
value of an option.
OK,
so for example, we plug these values in the model to obtain the theoretical
value of the July ABC 55 Call, and
we come up with a value of $5 ¼.
But wait, when we look at our monitor, we see that the actual market
price ( what the option is actually trading at), is only $5 even.
Using
a little high school algebra, we do the following.
We simply replace the theoretical value we just obtained with the actual
market price of the option, and run the pricing model in reverse.
We are thus effectively solving for the Volatility value that would be
needed to yield up a theoretical value that equals the actual market value of
the option. The number we come up with (
in % form) is the Implied Volatility value. Again,
this value tells us the volatility that the market is implying
for the underlying via its pricing of the specific option.
I
told you it was a little complicated. But
really Implied value is one of those features of volatility that professional
traders need to know more than the retail trader.
In a nutshell, the professional trader determines whether an option is
“overvaluedâ€, “undervalued†or at “fair value†by comparing the
Implied volatility value with the Future volatility value.
For the professional trader, if the Future Vol. is higher than the
implied vol, then the option is said to be
If the Future
vol. is lower than the implied vol, then the option is said
to be overvalued.
And if the Future. vol. is exactly equal to the Implied vol, then the
option is said to be at Note:
This does NOT mean that an option’s trader
merely buys the undervalued options and sells the overvalued ones like a monkey.
Much more goes into it than that. But
then that is the subject of a future lesson…
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