Title
Stability of central finite difference schemes on non-uniform grids for the Black-Scholes PDE with Neumann boundary condition
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York ,
Subject
Mathematics
Physics
Source (journal)
AIP conference proceedings / American Institute of Physics. - New York
Volume/pages
1479(2012) , p. 2178-2181
ISSN
0094-243X
ISI
000310698100514
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper concerns the numerical solution of the BlackScholes PDE with a Neumann boundary condition on the right boundary. We consider finite difference schemes for the semi-discretization, which leads to a system of ODEs with corresponding matrix M. In this paper stability bounds for exp(tM) (t ≥ 0) are proved. A scaled version of the Euclidean norm, denoted by ‖ ⋅ ‖H is considered. The advection and diffusion term of the PDE are analyzed separately. It turns out that the Neumann boundary condition leads to a growth of ‖exp(tM)‖H with the number of grid points m for the pure advection problem.
E-info
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Full text (open access)
https://repository.uantwerpen.be/docman/irua/9e15d4/101352.pdf
Handle