Most Efficient Homogeneous Volatility Estimators

21 Pages Posted: 9 Sep 2009

See all articles by Alexander I. Saichev

Alexander I. Saichev

ETH Zurich - D-MTEC (Deceased)

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)

Multiple version iconThere are 2 versions of this paper

Date Written: August 12, 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

Saichev, Alexander I. and Sornette, Didier and Filimonov, Vladimir, Most Efficient Homogeneous Volatility Estimators (August 12, 2009). Swiss Finance Institute Research Paper No. 09-35, Available at SSRN: https://ssrn.com/abstract=1470004 or http://dx.doi.org/10.2139/ssrn.1470004

Alexander I. Saichev

ETH Zurich - D-MTEC (Deceased)

Didier Sornette (Contact Author)

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

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Southern University of Science and Technology

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Tokyo Institute of Technology

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Vladimir Filimonov

Swiss Federal Institute of Technology Zurich (ETH Zurich) ( email )

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