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

Lookup NU author(s): Dr Xiaojing SongORCiD

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

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 ofthe singular diffusion processes on which the Feller papers are based.

Publication metadata

Author(s): Liu S, Melia A, Song X, Tippett M

Publication type: Article

Publication status: Published

Journal: European Journal of Finance

Year: 2020

Volume: 26

Issue: 9

Pages: 837-853

Online publication date: 12/01/2020

Acceptance date: 26/11/2019

Date deposited: 07/01/2021

ISSN (print): 1351-847X

ISSN (electronic): 1466-4364

Publisher: Routledge

URL: https://doi.org/10.1080/1351847X.2019.1709526

DOI: 10.1080/1351847X.2019.1709526

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