Merger, J.; Borzi, A. A Lie algebraic and numerical investigation of the Black-Scholes equation with Heston volatility model. (English) Zbl 1371.91180 J. Gen. Lie Theory Appl. 10, No. S2, Article ID 006, 7 p. (2016). Summary: 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. Cited in 1 Document MSC: 91G20 Derivative securities (option pricing, hedging, etc.) 35A30 Geometric theory, characteristics, transformations in context of PDEs 35K10 Second-order parabolic equations 37L20 Symmetries of infinite-dimensional dissipative dynamical systems Keywords:Lie algebra; Black-Scholes equation; differential equations; Lie symmetries; diffeomorphisms PDFBibTeX XMLCite \textit{J. Merger} and \textit{A. Borzi}, J. Gen. Lie Theory Appl. 10, No. S2, Article ID 006, 7 p. (2016; Zbl 1371.91180) Full Text: DOI Euclid