Chapter 36: The Basics of Volatility Trading 729 
underlying over the life of the option. The computation and comparison of these two 
measures can aid immensely in predicting the forthcoming volatility of the underly­
ing instrument - a crucial matter in determining today's option prices. 
Historical volatility can be measured with a specific formula, as shown in the · 
chapter on mathematical applications. It is merely the formula for standard deviation 
as contained in most elementary books on statistics. The important point to under­
stand is that it is an exact calculation, and there is little debate over how to compute 
historical volatility. It is not important to know what the actual measurement means. 
That is, if one says that a certain stock has a historical volatility of 20%, that by itself 
is a relatively meaningless number to anyone but an ardent statistician. However, it 
can be used for comparative purposes. 
The standard deviation is expressed as a percent. One can determine that the 
historical volatility of the broad stock market has usually been in the range of 15% to 
20%. A very volatile stock might have an historical volatility in excess of 100%. These 
numbers can be compared to each other, so that one might say that a stock with the 
latter historical volatility is five times more volatile that the "stock market." So, the 
historical volatility of one instrument can be compared with that of another instru­
ment in order to determine which one is more volatile. That in itself is a useful func­
tion of historical volatility, but its uses go much farther than that. 
Historical volatility can be measured over different time periods to give one a 
sense of how volatile the underlying has been over varying lengths of time. For exam­
ple, it is common to compute a 10-day historical volatility, as well as a 20-day, 50-day, 
and even 100-day. In each case, the results are annualized so that one can compare 
the figures directly. 
Consider the chart in Figure 36-2. It shows a stock (although it could be a 
futures contract or index, too) that was meandering in a rather tight range for quite 
some time. At the point marked "A" on the chart, it was probably at its least volatile. 
At that time, the 10-dayvolatility might have been something quite low, say 20%. The 
price movements directly preceding point A had been very small. However, prior to 
that time the stock had been more volatile, so longer-term measures of the historical 
volatility would shown higher numbers. The possible measures of historical volatility, 
then at point A, might have been something like: 
10-day historical volatility: 20% 
20-day historical volatility: 23% 
50-day historical volatility: 35% 
100-day historical volatility: 45% 
A pattern of historical volatilities of this sort describes a stock that has been 
slowing down lately.