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On the construction of a quartically convergent method for high-dimensional Black-Scholes time-dependent PDE

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  • Shi, Lei
  • Ullah, Malik Zaka
  • Nashine, Hemant Kumar

Abstract

There exist several numerical methods for finding the resolution of high dimensional option pricing Black-Scholes PDE with variable coefficients. Here we use radial basis functions to produce differentiation stencils (abbreviated by RBF-FD) on uniform point sets. In fact, the target is to propose a fully quartically convergent scheme via the RBF-FD methodology along both time and space directions. We too present a stability analysis for the selection of the time step size when the spatial step sizes vary. Furthermore, we draw a conclusion by several challenging computational experiments in high dimensions and reveal the superiority and the robustness of the scheme.

Suggested Citation

  • Shi, Lei & Ullah, Malik Zaka & Nashine, Hemant Kumar, 2024. "On the construction of a quartically convergent method for high-dimensional Black-Scholes time-dependent PDE," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005490
    DOI: 10.1016/j.amc.2023.128380
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    References listed on IDEAS

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    1. Gunter H Meyer, 2015. "The Time-Discrete Method of Lines for Options and Bonds:A PDE Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9292, October.
    2. Milovanović, Slobodan & von Sydow, Lina, 2020. "A high order method for pricing of financial derivatives using Radial Basis Function generated Finite Differences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 205-217.
    3. Lishang Jiang, 2005. "Mathematical Modeling and Methods of Option Pricing," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5855, February.
    4. Soleymani, Fazlollah & Akgül, Ali, 2019. "Improved numerical solution of multi-asset option pricing problem: A localized RBF-FD approach," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 298-309.
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