Angermann, Lutz Discretization of the Black-Scholes operator with a natural left-hand side boundary condition. (English) Zbl 1169.91360 Far East J. Appl. Math. 30, No. 1, 1-41 (2008). Summary: We propose a fitted finite volume discretization of the Black-Scholes differential operator, where the left-hand side boundary condition is treated as a natural boundary condition. For the case of European options, we describe a fully discrete method based on an implicit time stepping technique. The analysis is performed within the framework of the vertical method of lines, where the spatial discretization is formulated as a Petrov-Galerkin finite element method with each basis function of the trial space being determined by a set of two-point boundary value problems. We establish the stability and an error bound for the solutions of the fully discretized system. Cited in 6 Documents MSC: 91B28 Finance etc. (MSC2000) 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs Keywords:Black-Scholes equation; option valuation; fitted finite volume method PDFBibTeX XMLCite \textit{L. Angermann}, Far East J. Appl. Math. 30, No. 1, 1--41 (2008; Zbl 1169.91360) Full Text: Link