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.
"A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model." J. Gen. Lie Theory Appl. 10 (S2) 1 - 7, 2016. https://doi.org/10.4172/1736-4337.1000S2-006