alexa A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model | OMICS International | Abstract
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model

Merger J* and Borzi A

Research Assistant, Department of Mathematics, University of Würzburg, Chair for Scientific Computing Emil-Fischer-Straße 30, Room 02.013, 97074 Würzburg, Germany

Corresponding Author:
Merger J
Research Assistant, Department of Mathematics
University of Würzburg, Chair for Scientific Computing Emil-Fischer- Straße 30
Room 02.013, 97074 Würzburg, Germany
Tel: +499313180793
E-mail: [email protected]

Received date: December 19, 2015; Accepted date: January 25, 2016; Published date: January 27, 2016

Citation: Merger J, Borzi A (2016) A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model. J Generalized Lie Theory Appl S2:006. doi: 10.4172/2469-9837.1000S2-006

Copyright: © 2016 Merger J, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

This work deals with an extension of the Black-Scholes model for rating options with the Heston volatility model. A Lie-algebraic analysis of this equation is applied to reduce its order and compute some of its solutions. As a result of this method, a five-parameter family of solutions is obtained. Though, these solutions do not match the terminal and boundary conditions, they can be used for the validation of numerical schemes.

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