a pricing model is volatility. All of the other inputs-stock price, option
strike price, days until expiration, applicable interest rates, and dividends
-are essentially readily determinable. The validity of a pricing model's
output depends on the accuracy of all input amounts, but the quality of
the volatility input plays an important role. As the saying goes, "Garbage
in, garbage out." But what is the appropriate measure ofvolatility that we
should use? There are, in fact, a handful ofways in which we can measure
volatility.
The ideal volatility input for a pricing model would be the one that
most closely reflects the actual future movement of the underlying security.
Let's refer to this input as the future volatility: Absent a crystal ball,
however, we do not know the future volatility. Therefore, most traders
turn (for good measure) to the performance ofthe stock in the past, which
we call the historical volatility. Next, the trader will factor into the historical
volatility any special circumstances that he or she anticipates
prior to expiration. This foresight enables the trader to generate a forecast
volatility; which is essentially the trader's best guess at future volatility.
Armed with his or her forecast volatility, the trader is then able to
draw a comparison between the volatility indicated by the market price of
the option and the volatility determined by this market (referred to as the
implied volatility). Let's examine these measures more closely:
Measures of Volatility
Historical volatility; as its name implies, is a measure of actual price
changes in an underlying issue over a specific period in the past. Through
the statistical analysis ofhistorical data, a trader attempts to predict the
future volatility of the underlying issue. You should note, however, that
there is not just one measure of historic volatility. You can calculate historic
volatility over any time period that you choose. The trader will have
to decide which period(s) he or she wants to analyze: a week, a month, or
a year. In addition, he or she must also ask which price comparisons (closing
price to closing price, opening price to opening price, or the daily
highllow range) upon which he or she should base volatility assessments.
Different price comparisons will calculate different volatilities. Generally,
the trader calculates historical volatilities over both a short term (one to
two months) and a long term and then decides how to weight each calculation
when forecasting future volatility.
Expected/forecast volatility is what a trader attempts to predict based
upon his or her informed and/or educated speculation. More specifically;
forecast volatility is an estimate of the volatility of the underlying issue
for a specific period in the future. For most traders, the starting point of
volatility forecasting is a review of one or more historical volatilities.
Knowing that news events move markets, the trader adds to the equation
his or her assessment of how anticipated news events will affect volatility
For example, volatility usually rises in the period just prior to a quarterly
earnings announcement. If the company is the subject of a
government investigation or is involved in major litigation, you should
not ignore the possibility of news involving a major development. For
these reasons, volatility assessment is a highly subjective process that
offers no guarantee of accuracy.
Implied volatility is the marketplace's assessment of the future
volatility of the underlying issue. This implied volatility measures the
level of volatility that is implicitly assumed within the current market
price ofthe option. You could also consider implied volatility as a measure
of the market consensus of expected volatility of the underlying stock.
Implied volatility can be derived from running a pricing model backwards.
In other words, the trader can enter the current market price ofan
option into a pricing model along with the underlying price, strike price,
time until expiration, interest rate, and any applicable dividends. When
he or she then runs the model, then, it will solve for the unknown-the
volatility that the marketplace is using to price the option. This number
represents the implied volatility.
Implied volatility might or might not be equal to the future volatility
assumption ofan underlying issue. When the volatility assumption that we
are using to determine the theoretical value of an option differs from the
volatility that marketplace is using to determine the value ofan option, we
are able to enter all ofthe data into the pricing (as we have done below).
We exclude the volatility assumption and enter the theoretical value that
we have previously solved for in order to determine what volatility the marketplace
is giving the option.
In this example, we see that the marketplace has placed a higher
value on the March 40 call than on the trader who generated an informed
volatility prediction based on current movement in the underlying, historical
volatility and an expectation of market sentiment. What explains
this divergence? Generally; this disparity anticipation of news might
result in a large move in the price of the underlying issue (whether that
move is up or down).
Read More: Options Volatility
