This guide explains how to calculate historical volatility step by step, how to annualise it, how window length changes the result, a worked example and how to use HV in trading.
How historical volatility is calculated
- Collect closing prices for the period, such as the last 21 trading days.
- Calculate daily returns. The usual choice is the log return: ln(today's close ÷ yesterday's close).
- Calculate the standard deviation of those returns.
- Annualise by multiplying by the square root of the number of trading days in a year, about 252.
Annual HV = daily standard deviation × √252
A worked example
Suppose a stock's daily returns over the last month have a standard deviation of 0.9%.
Annual HV = 0.9% × √252 ≈ 0.9% × 15.87 ≈ 14.3%
At 14.3% annual volatility, a one standard deviation move over a year is about 14.3% of the price, and over one day about 0.9%.
Choosing the window
| Window | Behaviour |
|---|---|
| 10 days | Very responsive, noisy |
| 20 to 21 days | About a month, a common default |
| 60 days | About three months, smoother |
| 252 days | A year, slow to react |
A short window reacts quickly to new conditions but jumps around. A long window is stable but slow. Comparing two windows, such as 10-day and 60-day HV, shows whether volatility is rising or falling.
Other estimators
The close-to-close method ignores what happens during the day. Range-based estimators use the high and low as well:
- Parkinson uses each day's high and low, capturing intraday movement.
- Garman–Klass and similar estimators also use the open and close.
Range-based estimators can measure volatility more efficiently from the same number of days, though they are affected by gaps.
Historical vs implied volatility
| Historical volatility | Implied volatility | |
|---|---|---|
| What it measures | How much the price did move | How much the market expects it to move |
| Source | Past prices | Current option prices |
| Looks | Backward | Forward |
When implied volatility is well above recent historical volatility, options are priced for more movement than the market has recently shown, which option sellers may find attractive. When implied volatility is below historical volatility, options look cheap relative to recent movement. Neither guarantees what happens next. See the implied volatility calculator.
Using historical volatility in trading
- Position sizing: size positions inversely to volatility, so a more volatile stock gets a smaller position. See the position size calculator.
- Stops: set stops wider in volatile periods, or use ATR. See the ATR volatility strategy.
- Strategy filters: run breakout strategies when volatility is rising and mean reversion strategies when it is low and stable.
- Options pricing: use HV as a starting point for the volatility input in the Black-Scholes calculator.
- Comparing instruments: rank stocks by HV to understand their typical movement.
Limits of historical volatility
- The past is not the future. Volatility changes, often suddenly.
- It treats up and down moves the same. A strong rally raises HV just like a crash.
- Window choice changes the answer. Be consistent.
- Gaps and events can dominate short windows.
Start your free trial
Connect your broker, build a strategy and test it on paper before a single live order goes out.
Frequently asked questions
What is historical volatility?
The annualised standard deviation of an asset's past returns, showing how much its price has moved.
How do I annualise volatility?
Multiply the daily standard deviation by the square root of the number of trading days in a year, about 252.
What is a normal volatility for Nifty?
It varies with market conditions. Comparing current HV with its own range over the past year is more useful than a fixed number.
Is historical volatility the same as India VIX?
No. India VIX measures expected volatility from Nifty option prices. Historical volatility measures past movement in the index.
Sources
- Hull, J. C. Options, Futures, and Other Derivatives. Pearson
- Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53(1), 61–65
- Garman, M. B. and Klass, M. J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53(1), 67–78