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Discretization of the Black-Scholes operator with a natural left-hand side boundary condition. (English) Zbl 1169.91360

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.

MSC:

91B28 Finance etc. (MSC2000)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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