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A Robust Spline Collocation Method for Pricing American Put Options

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  • Zhongdi Cen
  • Anbo Le
  • Aimin Xu

Abstract

In this paper a robust numerical method is proposed for pricing American put options. The Black-Scholes differential operator in the original form is discretized by using a quadratic spline collocation method on a piecewise uniform mesh for the spatial discretization and the implicit Euler scheme for the time discretization. The position of collocation points is chosen so that the spline difference operator satisfies the discrete maximum principle, which guarantees that the scheme is maximum-norm stable. The error estimation is derived by applying the maximum principle to the discrete linear complementarity problem in two mesh sets. It is proved that the scheme is second-order convergent with respect to the spatial variable and first-order convergent with respect to the time variable. Numerical results demonstrate that the scheme is stable and accurate.

Suggested Citation

  • Zhongdi Cen & Anbo Le & Aimin Xu, 2019. "A Robust Spline Collocation Method for Pricing American Put Options," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-11, May.
    • Handle: RePEc:hin:jnddns:1753782
    DOI: 10.1155/2019/1753782
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    Cited by:

    1. Alghalith, Moawia, 2020. "Pricing the American options: A closed-form, simple formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).

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