What is realized volatility and how is it calculated?

The standard calculation

The most common method is close-to-close. Take the daily closing prices over the window, compute each day's return as the natural log of today's close divided by yesterday's, then compute the standard deviation of those returns. That gives a daily volatility. Multiply by the square root of 252, the approximate number of trading days in a year, to annualize it.

For example, if a stock's daily log returns over the past twenty sessions have a standard deviation of 1.5 percent, its twenty-day realized volatility is 1.5 times about 15.9, or roughly 24 percent annualized. That figure can be compared directly with the stock's implied volatility, which is quoted the same way.

Some calculations subtract the mean return before taking the standard deviation and some assume a mean of zero. Over short windows the difference is usually small, but it explains why two platforms can show slightly different figures for the same stock.

Range-based estimators

Close-to-close volatility ignores everything that happens during the day. A stock that swings five percent intraday but closes flat contributes nothing to it. Range-based estimators use each day's high and low, and sometimes the open, to capture more information from the same number of days.

The Parkinson estimator uses the daily high-low range. The Garman-Klass estimator adds the open and close. Others, such as Rogers-Satchell and Yang-Zhang, are designed to handle trending prices and overnight gaps more accurately. All of them are more statistically efficient than close-to-close, meaning they produce a stable estimate from fewer days of data.

The trade-off is sensitivity to bad prints. A single erroneous high or low in the data inflates a range-based estimate, while close-to-close is less exposed. Whichever estimator a tool uses, it should say so.

Choosing the window

Realized volatility depends heavily on the lookback. A ten-day window reacts quickly to a change in behaviour but is noisy. A sixty-day or ninety-day window is stable but slow, and can still reflect a market environment that ended weeks ago. Twenty or thirty days, roughly a month of trading, is a common middle ground and lines up with the horizon of most widely quoted implied volatility measures.

The window should match the question. If you are comparing realized volatility with the implied volatility of a 30-day option, a window of about the same length is the sensible pairing. If you are judging whether a stock's behaviour has changed, comparing a short window with a long one shows whether recent movement is above or below its longer norm.

Windows also behave strangely around single large days. An earnings gap enters a twenty-day window and then falls out of it twenty sessions later, creating a sudden drop in realized volatility that has nothing to do with the stock becoming calmer.

Overnight versus intraday

A stock's total volatility can be split into the moves that happen overnight, between one close and the next open, and the moves that happen during the session. For many single stocks, earnings and other news land outside trading hours, so a large share of their realized volatility comes from gaps.

That split matters for anyone trading intraday. A stock with high close-to-close volatility driven mostly by overnight gaps can still be relatively calm during the session. Conversely, a name with modest close-to-close volatility can have wide intraday ranges that reverse by the close.

Range-based estimators that ignore the open miss overnight gaps entirely, while close-to-close captures them but misses intraday swings. That is part of why estimators such as Yang-Zhang combine the overnight component with an intraday range component: it gives a fuller picture of total movement for names whose risk is split between the two.

Realized against implied

On average, implied volatility has tended to exceed the realized volatility that follows it, a gap known as the variance risk premium. Option sellers demand compensation for carrying the risk of sudden large moves, and buyers are willing to pay for protection.

That average hides a lot. Realized volatility tends to cluster: calm periods follow calm periods and turbulent periods follow turbulent ones, so a stock that has just started moving more than usual can deliver more than its implied volatility charged. The comparison is most useful as an ongoing measurement for each ticker, not as a fixed rule that implied is always too high.