Journal of Generalized Lie Theory and Applications

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

J Merger and A Borzi

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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.

Article information

Source
J. Gen. Lie Theory Appl., Volume 10, Number S2 (2016), 7 pages.

Dates
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1479265225

Digital Object Identifier
doi:10.4172/1736-4337.1000S2-006

Mathematical Reviews number (MathSciNet)
MR3663975

Zentralblatt MATH identifier
1371.91180

Keywords
Lie algebra Black-Scholes equation Differential equations Lie symmetries Diffeomorphisms

Citation

Merger, J; Borzi, A. A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model. J. Gen. Lie Theory Appl. 10 (2016), no. S2, 7 pages. doi:10.4172/1736-4337.1000S2-006. https://projecteuclid.org/euclid.jglta/1479265225


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