Realised Volatility Estimators and Their Trade Offs

Close-to-close, Parkinson, Garman-Klass, Rogers-Satchell and Yang-Zhang trade statistical efficiency against sensitivity to drift, gaps and noise.

Realised volatility can be measured more efficiently than the standard close-to-close standard deviation by using the high, low, open and close of each period, and the choice between estimators such as Parkinson, Garman-Klass, Rogers-Satchell and Yang-Zhang trades off statistical efficiency against sensitivity to microstructure noise and to jumps between sessions, so no single estimator is correct for every use.

The standard estimator takes the log return between each pair of consecutive closes over a chosen window, squares each one, sums them, scales by 252 divided by the number of observations, and takes the square root. It uses only the closing price of each session and discards everything that happened intraday, which makes it statistically inefficient: the standard error on the estimate falls only slowly as more days are added. A 20-day close-to-close estimate carries a relative standard error on the order of 16 percent from sampling noise alone, meaning a true underlying volatility of 20 percent can print anywhere from roughly 17 to 23 percent purely by chance, before any real change in the…

The Parkinson estimator replaces the close-to-close return with the log of the day’s high divided by the day’s low, which captures the full range the price travelled during the session rather than only where it started and ended. Because the range carries far more information about intraday movement than a single close-to-close return does, the Parkinson estimator is commonly cited as roughly five times more statistically efficient than close-to-close, meaning it reaches the same precision with around a fifth of the data. The trade-off is that it assumes no overnight drift between sessions and ignores gaps between one day’s close and the next day’s open entirely, so it understates…

The Garman-Klass estimator adds the open and the close into the same range-based framework, pushing the cited efficiency gain over close-to-close toward roughly seven times, at the cost of still assuming zero drift within each session, an assumption that biases the estimate on a strongly trending name. Rogers-Satchell removes that zero-drift assumption directly, building a formula from the open, high, low and close that stays unbiased whether the underlying trended up, down or sideways during the session, which makes it the better choice for anything with a persistent directional move, though like Parkinson it still has no mechanism for handling a gap between one close and the next open.

The Yang-Zhang estimator combines a separate measurement of overnight, close-to-open volatility with the Rogers-Satchell intraday measurement, weighting the two components to minimise the total variance of the combined estimate. It is both drift-independent and able to account for the jump that happens while a market is closed, which the range-based estimators before it cannot see at all, and the original derivation cites an efficiency gain over close-to-close that can reach an order of magnitude or more depending on how much of the day’s total variance sits in the overnight gap versus the trading session itself.