Convergence of a fitted finite volume method for the penalized Black–Scholes equation governing European and American Option pricing |
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Authors: | Lutz Angermann Song Wang |
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Institution: | 1. Institut für Mathematik, Technische Universit?t Clausthal, Erzstra?e 1, 38678, Clausthal-Zellerfeld, Germany 2. School of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Crawley, WA, 6009, Australia
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Abstract: | In this paper we present an analysis of a numerical method for a degenerate partial differential equation, called the Black–Scholes
equation, governing American and European option pricing. The method is based on a fitted finite volume spatial discretization
and 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. Numerical results are presented to validate the theoretical results. |
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Keywords: | 65 M 60 65 K 10 90 C 33 |
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