Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

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


Merger J and Borzi A

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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