Meshfree RBF-FD Discretization with Three-Point Stencils for Nonlinear Pricing Options Having Transaction Costs

Haifa Bin Jebreen (), Yurilev Chalco-Cano and Hongzhou Wang
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Haifa Bin Jebreen: Mathematics Department, College of Science, King Saud University, Riyadh P.O. Box 145111, Saudi Arabia
Yurilev Chalco-Cano: Departamento de Matemática, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile
Hongzhou Wang: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2025, vol. 13, issue 17, 1-15

Abstract: This paper presents a computational framework for resolving a nonlinear extension of the Black–Scholes partial differential equation that accounts for transaction costs through a volatility function dependent on the Gamma of the option price. A meshfree radial basis function-generated finite difference procedure is developed using a modified multiquadric kernel. Analytical weight formulas for first- and second-order differentiations are discussed on 3-node stencils for both uniform and non-uniform point distributions. The proposed method offers an efficient scheme suitable for accurately pricing European scenarios when nonlinear transaction cost effects.

Keywords: nonlinear Black–Scholes; RBF-FD method; transaction costs; volatility; high-order numerical scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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