Most Efficient Homogeneous Volatility Estimators

Saichev, Alexander I.; Sornette, Didier; Filimonov, Vladimir

doi:10.2139/ssrn.1596036

Most Efficient Homogeneous Volatility Estimators

CCSS Working Paper Series No. CCSS-09-007

20 Pages Posted: 27 Apr 2010

See all articles by Alexander I. Saichev

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute; Southern University of Science and Technology; Tokyo Institute of Technology

Vladimir Filimonov

Swiss Federal Institute of Technology Zurich (ETH Zurich)

There are 2 versions of this paper

Date Written: October 25, 2009

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

Suggested Citation: Suggested Citation

Saichev, Alexander I. and Sornette, Didier and Filimonov, Vladimir, Most Efficient Homogeneous Volatility Estimators (October 25, 2009). CCSS Working Paper Series No. CCSS-09-007, Available at SSRN: https://ssrn.com/abstract=1596036 or http://dx.doi.org/10.2139/ssrn.1596036