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

Siqi Liu, Adrian Melia, Xiaojing Song and Mark Tippett

The European Journal of Finance, 2020, vol. 26, issue 9, 837-853

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.

Date: 2020
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DOI: 10.1080/1351847X.2019.1709526

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