Historical Volatility
The realised standard deviation of an underlying's returns over a past period, annualised.
Formula
Historical Volatility = Standard Deviation of Daily Log Returns x square root of 252, expressed as a percentage
Unit
%
In depth
Historical volatility measures what actually happened while implied volatility measures what options are priced for, and the gap between them is the volatility risk premium — implied has tended to exceed realised on average, which is the statistical basis for option writing being profitable most of the time. The annualisation factor uses the square root of the number of trading days because variance scales with time while standard deviation scales with its square root. The measure is backward-looking and assumes the past window is representative, which it is not around regime changes. Comparing the two volatilities is more informative than either alone.
Worked example
Daily returns with a standard deviation of 0.85% annualise to 0.85% x square root of 252 = 0.85 x 15.87 = 13.5%. If options are implying 17%, the market is charging 3.5 points above what has recently been realised.
Illustrative figures, chosen so the arithmetic is easy to follow. Not a live price and not a valuation of any company.
Educational reference only
This entry explains what “Historical Volatility” means. It is not investment advice and not a recommendation to buy or sell any security. Any numbers above are illustrative, not live prices, and nothing here predicts price direction or rates a stock. Consider your own circumstances and consult a SEBI-registered investment adviser before acting.