Historical and Realized Volatility

Historical volatility, also called realised volatility, measures how much an asset's price has actually moved over a past period. It is usually expressed as an annualised standard deviation of returns, the same units as implied volatility, so the two can be compared directly. Traders use historical volatility to judge whether options are cheap or expensive, to size positions and to understand how a market's behaviour is changing. The general idea of volatility is introduced in Volatility.

The standard calculation#

1. Collect closing prices for the period, such as the last 21 trading days.
2. Compute log returns: r = ln(P_today / P_yesterday).
3. Compute the standard deviation of those returns. See Variance and Standard Deviation.
4. Annualise by multiplying by the square root of the number of trading periods per year, usually √252 for daily data.

historical volatility = stdev(daily log returns) × √252

Choosing the window#

Shorter windows react quickly but are noisy; longer windows are stable but slow to reflect change. Comparing several windows shows whether volatility is rising or falling. See Rolling and Expanding Windows.

Range based estimators#

Close to close volatility ignores what happened during the day. Estimators that use the high, low and open can be more efficient, meaning they need fewer days for the same accuracy:

The ATR (Average True Range) indicator is a related range based measure used in trading, expressed in price units rather than annualised percentages.

Intraday realised volatility#

With high frequency data, realised volatility can be computed by summing squared intraday returns, for example every five minutes. This gives accurate daily volatility estimates and is widely used in research. Very frequent sampling can be distorted by bid ask bounce, so five minute sampling is a common compromise.

How traders use historical volatility#

• Compare with implied volatility: if implied is well above recent realised, options may be expensive; if below, cheap. See Implied Volatility (IV).
• Position sizing: risk the same amount per trade by sizing inversely to volatility. See Volatility and ATR-Based Sizing.
• Regime awareness: rising volatility often comes with falling equity prices and wider spreads. See Structural Breaks and Regime Changes.
• Forecasting: models such as GARCH use the clustering of volatility, where calm follows calm and turbulence follows turbulence, to forecast it. See GARCH.

Limitations#

• Backward looking: it tells you what happened, not what will happen.
• Sensitive to window and method.
• Single events dominate: one huge day can lift a 21 day measure for a month, then drop out suddenly.
• Gaps and illiquid closes can distort close to close estimates.

Frequently asked questions#

What is historical volatility?#

A measure of how much an asset's price actually moved over a past period, usually the annualised standard deviation of daily log returns.

How is historical volatility calculated?#

Compute daily log returns over a window, take their standard deviation and multiply by the square root of 252 to annualise.

What is the difference between historical and implied volatility?#

Historical volatility measures past movement from prices; implied volatility is the expected future movement priced into options.

Next, learn how to judge whether today's implied volatility is high or low in IV Rank and IV Percentile.