Cubic Spline Method for a Generalized Black-Scholes Equation

Jian Huang and Zhongdi Cen

Mathematical Problems in Engineering, 2014, vol. 2014, 1-7

Abstract:

We develop a numerical method based on cubic polynomial spline approximations to solve a a generalized Black-Scholes equation. We apply the implicit Euler method for the time discretization and a cubic polynomial spline method for the spatial discretization. We show that the matrix associated with the discrete operator is an M-matrix, which ensures that the scheme is maximum-norm stable. It is proved that the scheme is second-order convergent with respect to the spatial variable. Numerical examples demonstrate the stability, convergence, and robustness of the scheme.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:484362

DOI: 10.1155/2014/484362

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