Singular diffusions, constant elasticity of variance processes and logarithmic rates of return

Siqi Liu, Adrian Melia, Xiaojing Song, Mark Tippett

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Abstract

The singular diffusion processes developed by William Feller occupy a central role in a number of disciplines including economics and finance. We identify a fundamental inconsistency between the probability densities stated in the Feller papers for these singular diffusion processes. Moreover, we apply the method of group-invariance to resolve this inconsistency. Since logarithmic returns are of considerable importance in economics and finance, we also illustrate a procedure for determining the conditional expected logarithmic rate of return for state variables which evolve in terms of the singular diffusion processes on which the Feller papers are based.
Original languageEnglish
Pages (from-to)837-853
JournalEuropean Journal of Finance
Volume26
Issue number9
Early online date12 Jan 2020
DOIs
Publication statusPublished - Sep 2020

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