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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Haifa Bin Jebreen & Yurilev Chalco-Cano & Hongzhou Wang, 2025. "Meshfree RBF-FD Discretization with Three-Point Stencils for Nonlinear Pricing Options Having Transaction Costs," Mathematics, MDPI, vol. 13(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2839-:d:1741059
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