Stability of central finite difference schemes on non-uniform grids for the Black-Scholes PDE with Neumann boundary conditionStability of central finite difference schemes on non-uniform grids for the Black-Scholes PDE with Neumann boundary condition
Faculty of Sciences. Mathematics and Computer Science
Applied mathematics and numerical analysis
2012New York, 2012
AIP conference proceedings / American Institute of Physics. - New York
1479(2012), p. 2178-2181
University of Antwerp
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.