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Historical volatility is the volatility of a financial instrument based on historical returns.
Volatility
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| Historical volatility calculation using close-to-close prices. full text » |
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| The Parkinson formula for estimating the historical volatility of an underlying based on high and low prices. full text » |
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| Yang and Zhang derived an extension to the Garman Glass historical volatility estimator that allows for opening jumps. It assumes Brownian motion with zero drift. This is currently the preferred version of open-high-low-close volatility estimator for zero drift and has an efficiency of 8 times the classic close-to-close estimator. Note that when the drift is nonzero, but instead relative large to the volatility, this estimator will tend to overestimate the volatility. full text » |
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| The Garman and Klass estimator for estimating historical volatility assumes Brownian motion with zero drift and no opening jumps (i.e. the opening = close of the previous period). This estimator is 7.4 times more efficient than the close-to-close estimator. full text » |
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| The Roger and Satchell historical volatility estimator allows for non-zero drift, but assumed no opening jump. full text » |
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| 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.
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