Yang and Zhang were the first to derive an historical volatility estimator that has a minimum estimation error, is independent of the drift, and independent of opening gaps. This estimator is maximally 14 times more efficient than the close-to-close estimator. It can be interpreted as a weighted average of the Rogers and Satchell estimator, the close-open volatility and the open-close volatility. The performance degrades to the classic close-to-close estimator when the price process is heavily dominated by opening jumps.

List of symbols

	Volatility
Z	Number of closing prices in a year
n	Number of historical prices used for the volatility estimate
	The opening price
	The high
	The low
	The close

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