# Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility

^{1}

Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia 5090000, Chile

^{2}

Department of Mathematics, Pondicherry University, Kalapet 605014, India

^{3}

Institute of Systems Science, Department of Mathematics, Durban University of Technology, Durban 4000, South Africa

^{4}

School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa

^{5}

Department of Mathematics and Statistics, University of Cyprus, Lefkosia 1678, Cyprus

^{†}

These authors contributed equally to this work.

^{*}

Author to whom correspondence should be addressed.

Academic Editor: Indranil SenGupta

Received: 30 January 2016 / Revised: 14 April 2016 / Accepted: 15 April 2016 / Published: 3 May 2016

(This article belongs to the Special Issue Mathematical Finance)

# Abstract

We perform a classification of the Lie point symmetries for the Black-Scholes-Merton Model for European options with stochastic volatility,*Keywords:*lie point symmetries; financial mathematics; stochastic volatility; Black-Scholes-Merton equation

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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**MDPI and ACS Style**

Paliathanasis, A.; Krishnakumar, K.; Tamizhmani, K.; Leach, P.G. Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility. *Mathematics* **2016**, *4*, 28.

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