Past Observance

The standard deviation of percentage changes in price is used to calculate observed volatility within the considered timeframe.

Trading range

Historical volatility uses historical (daily, weekly, monthly, quarterly, and yearly) price data to empirically measure the volatility of a market or instrument in the past. The value rendered by a historical volatility study is the standard deviation of bar-to-bar price differences.

Calculation

Standard Deviation, or Historical Volatility:

Where:
s = standard deviation, or historical volatility
n = number of occurrences (bars)
m = mean
xi = price changes
And:
Mean:

Where:
m = mean
n = number of occurrences
xi = price changes
And:
xi can equal percent of price change:

Or:
xi can equal natural logarithmic price change:

Applications

The independent research team sought to determine in association with our analysts whether there is a simple alternative estimator, that is onesimple enough to calculate using standard spreadsheet software, which provides a better volatility estimate to use in option pricing modelsthan the historical standard deviation.
They have found that when log-returns are approximatelynormally distributed there is - specifically, the adjusted mean absolute return deviation, which is13the absolute mean return deviation multiplied by the square root of Π/2. In all except the short terminterest rate market where the deviation from log-normality is most serious, the adjusted meanabsolute deviation forecasts actual volatility consistently better than the historical standarddeviation.

They also found that this simple estimator compares very favorably with GARCH modelestimates. By one measure of forecast accuracy, the adjusted mean absolute return deviation beatsGARCH consistently, while by the other measure, they approximately break even.

They’ll continue to publish their research on this topic over time.