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High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation

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  • Yuri M. Dimitrov
  • Lubin G. Vulkov

Abstract

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed.

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  • Yuri M. Dimitrov & Lubin G. Vulkov, 2016. "High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation," Papers 1604.05178, arXiv.org.
    • Handle: RePEc:arx:papers:1604.05178
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Chinonso Nwankwo & Weizhong Dai & Tony Ware, 2023. "Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping," Papers 2309.03984, arXiv.org, revised Sep 2023.

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