Drift Independent Volatility Estimation Based on High, Low, Open, and Close Prices

Abstract

We present a new volatility estimator based on multiple periods of high, low, open, and close prices in a historical time series. The new estimator has the following nice properties: it is (a) unbiased in the continuous limit, (b) independent of the drift, (c) consistent in dealing with opening price jumps. Furthermore, it has the smallest variance among all estimators with similar properties. The improvement of accuracy over the classical close‐to‐close estimator is dramatic for real‐life time series.