Realized Volatility and Implied Volatility:
Similarities and Differences
In all discussions pertaining to the various forms of volatility
trading, be they hedging, speculation, or investing, we must be
careful to distinguish between the two most commonly recognized
varieties of volatility: actual — often referred to
as historical, realized, market, or stock volatility — and
implied, which is derived from the prices of options. We
shall discuss briefly how each form of volatility is calculated,
and then explore some of the most obvious similarities and differences
between the two.
Realized Volatility Calculation
There are a few ways in which to determine realized, market,
or actual volatility. The RealVol daily formula
adopted by The Volatility Exchange uses a traditional standard
deviation calculation, assuming a mean of zero for the return
of the underlying asset. For example, the daily return of an average
stock, or stock index, is slightly lower than onetwentieth of
one percent (0.05%), so using a mean of zero has little effect
on the ultimate volatility value obtained by the formula, while
it greatly facilitates the calculation. Please see our various
volatility graphs and volatility
charts for a further appreciation of the onemonth, threemonth,
and oneyear historical volatilities of a wide variety of underlying
assets.
To date, there has not been an exchangetraded realizedvolatility
futures contract. RealVol futures, options, and futureslike instruments settling
to the realized volatility of an underlying, will bridge this
gap and provide the world's investment community with the first
such listed products.
Implied Volatility Calculation: Implied Volatility Explained
It is interesting to note that, unlike the case for realized
volatility, there is no straightforward formula for actually calculating
implied volatility. We don’t really calculate implied volatility
as much as we observe option volatility, or a volatility
index, such as VIX, designed to represent the implied volatility
of an array of options. Since a volatility estimate is required
as one of the inputs into the BlackScholes
optionpricing model (for options on stocks) or the Black
Model (for options on futures), if, instead, we suppose that
the observable market price of the option is an input,
we “trick” the options model into furnishing the option volatility
assumption that was used to price the option in the first place.
In essence, we obtain the option's implied volatility by running
the option model “backwards.”
So, the best answer to the question, “What is implied volatility?”
is: the volatility that one would have to input into the options
pricing model in order to arrive at the current option price.
Comparisons and Contrasts
It is an observable phenomenon that, for the most part, the implied
volatility surface for a wide range of options on a specific underlying
asset averages to a value that is somewhat higher (sometimes significantly
so) than the typical volatility that the asset eventually displays
(the realized volatility). One explanation for this implied volatility/realized
volatility “premium,” or gap, is that sellers of naked options
bear an openended, unlimited risk and, therefore, command from
the buyers, whose risk is predetermined and limited, some form
of extra compensation.
Indeed, as RealVol futures trade, it is interesting to note how their pricing reflects such a premium, and how that premium varies over time as one enters and moves through the RealVol calculation period (CP) (see our Glossary).
Many of the fascinating studies catalogued in our Volatility
Links and Volatility
Library sections address the issue of historical implied volatility
and its relationship to actual asset volatility.
The Variability of Volatility Itself
Whether implied or realized, there is a stochastic, or random,
component to volatility. “Stochastic volatility” refers to the
tendency for volatility to fluctuate over time. Indeed, this “volatility
of volatility” (“vol of vol”) can be quite pronounced and often
furnishes traders of implied volatility options with ample opportunities
for profit. In similar fashion, it is expected that the onemonth
RealVol futures (1VOL), whose annualized realized volatility
can be very large, often ranging between 80%–100%, will provide
potential investors and speculators with the ability to trade
a vehicle that exhibits almost unprecedented levels of variability itself.
Finally, one must also appreciate the similarity that exists
between RealVol futures and overthecounter (OTC) volatility swaps. Volatility swaps and the closely related
product variance swaps enjoy considerable popularity, but their
access is often closed to the broad trading public. RealVol futures
will provide the opportunity for many to experience the benefits
of volatility swaps in a listed, easily accessible,
but hitherto unavailable, environment.


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