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A New High-Order Compact Finite Difference Scheme for Solving Black-Scholes Equation

In: Proceedings of 20th International Conference on Industrial Engineering and Engineering Management

Author

Listed:
  • Lu-feng Yang

    (Beifang University of Nationalities)

  • Xu-lin Hu

    (Beifang University of Nationalities)

Abstract

Richardson extrapolation is a commonly used technique in financial applications for accelerating the convergence of numerical methods. In this paper an unconditionally stable high-order compact finite difference scheme is proposed for solving the Black-Scholes equation, and the convergence rate is second-order in time and fourth-order in space. Then a Richardson extrapolation algorithm develops to make the final computed solution sixth-order accurate both in time and space when the time step equals the spatial mesh size. Numerical experiments show the effectiveness of the method.

Suggested Citation

  • Lu-feng Yang & Xu-lin Hu, 2013. "A New High-Order Compact Finite Difference Scheme for Solving Black-Scholes Equation," Springer Books, in: Ershi Qi & Jiang Shen & Runliang Dou (ed.), Proceedings of 20th International Conference on Industrial Engineering and Engineering Management, edition 127, pages 1007-1019, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-40063-6_99
    DOI: 10.1007/978-3-642-40063-6_99
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