Geometric Mean Reversion: Formulas for the Equilibrium Density and Analytic Moment Matching

Ewald, Christian Oliver; Yang, Zhaojun

doi:10.2139/ssrn.999561

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Geometric Mean Reversion: Formulas for the Equilibrium Density and Analytic Moment Matching

25 Pages Posted: 11 Jul 2007

See all articles by Christian Oliver Ewald

Christian Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Zhaojun Yang

Southern University of Science and Technology - Department of Finance

Date Written: July 10, 2007

Abstract

We study the classical geometric mean reversion process which has been used to model commodity prices by various authors in Economics and Finance. We obtain certain regularity results which guarantee positivity and the existence of a stationary distribution. More important we derive an analytical formula for the stationary distribution and all of its higher moments. Furthermore we derive a computationally simple but efficient recursive formula for the higher moments which we apply to moment matching.

Keywords: Models of mean-reversion, equilibrium distributions

JEL Classification: C13, C16, C61

Suggested Citation: Suggested Citation

Ewald, Christian Oliver and Yang, Zhaojun, Geometric Mean Reversion: Formulas for the Equilibrium Density and Analytic Moment Matching (July 10, 2007). Available at SSRN: https://ssrn.com/abstract=999561 or http://dx.doi.org/10.2139/ssrn.999561