Estimating Historical Volatility

The research considers the properties of a number of statistical measures of volatility, extending from the common standard deviation metric to less widely used range-based measures. Prior research in this field, which has typically featured the use of data series generated by Monte Carlo simulation within the theoretical framework of Geometric Brownian Motion, has tended towards the conclusion that alternate volatility estimators offer substantial efficiency improvements relative to the standard deviation estimator. This research indicates, however, that such findings are critically dependent on the assumptions made with regard to the nature of the underlying process of interest. The research considers the effect that departures from the behavior of the idealized Geometric Brownian Motion process may have on the performance of a variety of volatility estimators. More specifically, we evaluate the impact that sample size and frequency, process drift, opening gaps and time-varying volatility may have on the performance of both the standard deviation metric and its various alternatives. Under each of the scenarios considered, the integrated volatility estimator represents the “gold standard” in terms of bias and efficiency. All other estimators, with the possible exception of the Alizadeh-Brandt-Diebold estimator, produce biased estimates of the true process volatility unless