Chapter 36: The Basics of Volatility Trading 731 
probability models. We need to be able to make volatility estimates in order to deter­
mine whether or not a strategy might be successful, and to determine whether the 
current option price is a relatively cheap one or a relatively expensive one. For exam­
ple, one can't just say, "I think XYZ is going to rise at least 18 points by February expi­
ration." There needs to be some basis in fact for such a statement and, lacking inside 
information about what the company might announce between now and February, 
that basis should be statistics in the form of volatility projections. 
Historical volatility is, of course, useful as an input to the (Black-Scholes) option 
model. In fact, the volatility input to any model is crucial because the volatility com­
ponent is such a major factor in determining the price of an option. Furthermore, 
historical volatility is useful for more than just estimating option prices. It is neces­
sary for making stock price projections and calculating distributions, too, as will be 
shown when those topics are discussed later. Any time one asks the question, "What 
is the probability of the stock moving from here to there, or of exceeding a particu­
lar target price?" the answer is heavily dependent on the volatility of the underlying 
stock (or index or futures). 
It is obvious from the above example that historical volatility can change dra­
matically for any particular instrument. Even if one were to stick with just one 
measure of historical volatility ( the 20-day historical is commonly the most popular 
measure), it changes with great frequency. Thus, one can never be certain that bas­
ing option price predictions or stock price distributions on the current historical 
volatility will yield the "correct" results. Statistical volatility may change as time 
goes forward, in which case your projections would be incorrect. Thus, it is impor­
tant to make projections that are on the conservative side. 
ANOTHER APPROACH: GARCH 
GARCH stands for Generalized Autoregressive Conditional Heteroskedasticity, 
which is why it's shortened to GARCH. It is a technique for forecasting volatility that 
some analysts say produces better projections than using historical volatility alone or 
implied volatility alone. GARCH was created in the 1980s by specialists in the field of 
econometrics. It incorporates both historical and implied volatility, plus one can throw 
in a constant ("fudge factor"). In essence, though, the user of GARCH volatility mod­
els has to make some predictions or decisions about the weighting of the factors used 
for the estimate. By its very nature, then, it can be just as vague as the situations 
described in the previous section. 
The model can "learn," though, if applied correctly. That is, if one makes a 
volatility prediction for today (using GARCH, let's say), but it turns out that the actu-