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Cubic Spline Method for a Generalized Black-Scholes Equation

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  • Jian Huang
  • Zhongdi Cen

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.

Suggested Citation

  • Jian Huang & Zhongdi Cen, 2014. "Cubic Spline Method for a Generalized Black-Scholes Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlmpe:484362
    DOI: 10.1155/2014/484362
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    Cited by:

    1. Ruyi Xing & Meng Liu & Kexin Meng & Shuli Mei, 2021. "Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model," Mathematics, MDPI, vol. 9(14), pages 1-15, July.

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