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

Lei Shi, Malik Zaka Ullah and Hemant Kumar Nashine

Applied Mathematics and Computation, 2024, vol. 463, issue C

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.

Keywords: High-dimensional Black-Scholes; Quartically convergent; Stability; Discretization; Payoff (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005490

DOI: 10.1016/j.amc.2023.128380

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