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Geometric Mean Reversion: Formulas for the Equilibrium Density and Analytic Moment Matching
Christian-Oliver Ewald Center for Dynamic Macroeconomic Analysis, University of St. Andrews, School of Economics and Finance; University of Sydney, School of Mathematics and Statistics Zhaojun Yang Hunan University - School of Economics and Trade 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 Classifications: C13, C16, C61 Working Paper SeriesDate posted: July 11, 2007 ; Last revised: September 10, 2007Suggested CitationContact Information
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