Most Efficient Homogeneous Volatility Estimators

Abstract

We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval by the joint distributions of the high-minusopen, low-minus-open and close-minus-open values, whose analytical expression is derived exactly for Wiener processes with drift. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass, Roger-Satchell and maximum likelihood estimators.

Keywords: Variance and volatility estimators, efficiency, homogeneous functions, Schwarz inequality, extremes of Wiener processes

JEL Classification: C13, C51