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A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Node

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  • Amirhossein Sobhani
  • Mariyan Milev

Abstract

In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date could be calculate by computing a recursive integral formula upon the heat equation solution. We have approximated these recursive solutions with the aim of Lagrange interpolation on Jacobi polynomials node. After that, an operational matrix, that makes our computation significantly fast, has been driven. The most important feature of this method is that its CPU time dose not increase when the number of monitoring dates increases. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.

Suggested Citation

  • Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Node," Papers 1712.01060, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1712.01060
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    References listed on IDEAS

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    Cited by:

    1. H. Mesgarani & M. Bakhshandeh & Y. Esmaeelzade Aghdam & J. F. Gómez-Aguilar, 2023. "The Convergence Analysis of the Numerical Calculation to Price the Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1845-1856, December.
    2. Ahmad Golbabai & Omid Nikan, 2020. "A Computational Method Based on the Moving Least-Squares Approach for Pricing Double Barrier Options in a Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 119-141, January.
    3. Ahmadian, D. & Farkhondeh Rouz, O. & Ivaz, K. & Safdari-Vaighani, A., 2020. "Robust numerical algorithm to the European option with illiquid markets," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. Guillaume Leduc, 2024. "The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing," Mathematics, MDPI, vol. 12(7), pages 1-15, March.

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