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<p>This research presents a novel approach to the option-pricing problem within the framework of jump-diffusion models. The proposed numerical methodology addresses the partial integro-differential equation (PIDE) associated with pricing European options. By employing an implicit–explicit time discretization scheme, the method integrates the radial basis function-based finite-difference (RBF-FD) technique, augmented with polynomial terms for spatial discretization. The study utilizes both infinitely smooth RBFs, such as Gaussian and inverse quadratic, as well as piecewise smooth RBFs, including thin plate spline and natural cubic spline, combined with polynomials. Comparative analyses demonstrate that the proposed method achieves significantly reduced computational errors and faster execution times compared to earlier works, highlighting its superior accuracy and efficiency.</p>

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A robust RBF-FD technique combined with polynomial enhancements for valuing European options in jump-diffusion frameworks

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • Narges Hosseinzadeh,
  • Elyas Shivanian,
  • Mohammad Z. Fairooz,
  • Tannaz G. Chegini

摘要

This research presents a novel approach to the option-pricing problem within the framework of jump-diffusion models. The proposed numerical methodology addresses the partial integro-differential equation (PIDE) associated with pricing European options. By employing an implicit–explicit time discretization scheme, the method integrates the radial basis function-based finite-difference (RBF-FD) technique, augmented with polynomial terms for spatial discretization. The study utilizes both infinitely smooth RBFs, such as Gaussian and inverse quadratic, as well as piecewise smooth RBFs, including thin plate spline and natural cubic spline, combined with polynomials. Comparative analyses demonstrate that the proposed method achieves significantly reduced computational errors and faster execution times compared to earlier works, highlighting its superior accuracy and efficiency.