A Computational Method to Generate a Family of Extreme-Value Volatility Estimators

A framework is developed to construct estimators of volatility derived from extreme prices of a security, such as high, low, opening, and closing prices, using null space decomposition. This framework not only reproduces the classical estimators, such as the Parkinson (1980) and Garman and Klass (1980) estimators, but also improves the efficiency of some of the classical estimators, including the Parkinson (1980) estimator. The estimator that utilizes only high and low prices, as derived from this method, achieves a 17% reduction in variance compared to Parkinson (1980), which also utilizes high and low prices. Extension of this framework is possible to cases where prices are observed to drift and discontinuities in prices exist, due to the close of the trading day.