Option Pricing under the Heston Model Using Generalized Gaussian Radial Basis Functions with Variable Shape Parameters

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

2 Department of Financial Mathematics, Faculty of Financial Sciences, Kharazmi University, P.O. Box 15936-56311, Tehran, Iran.

Abstract

This work offers a new numerical method for solving the Heston stochastic volatility equation used for European and American option pricing problems through radial basis function (RBF) collocation, utilizing Generalized Gaussian radial basis functions (GGRBF) with variable shape parameters. The Heston model uses a mean-reverting square-root diffusion process for describing volatility and represents a significant advancement over the Black–Scholes model, since it represents market reality more accurately through a non-constant volatility process.

To improve numerical efficiency and mitigate ill-conditioning in the collocation matrices, this work combines Generalized Gaussian RBFs with a Symmetric Variable Shape Parameter (SVSP) strategy.

Generalized Gaussian RBFs are a generalization of Gaussian RBFs and consist of an additional shape parameter, increasing flexibility without losing differentiability. The Symmetric Variable Shape Parameter method improves numerical efficiency and reduces ill-conditioning effects by assigning a distinct shape parameter for each distinct RBF node position. Time discretization is completed using the implicit theta-method and radial basis function collocation for spatial approximation. The work includes a complete convergence and stability analysis and verifies the results through numerical experiments confirming the advantages of the new approach over conventional Gaussian RBFs with fixed shape parameters and the discontinuous Galerkin finite element method (dGFEM).

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 16 May 2026

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History

  • Receive Date: 22 December 2025
  • Revise Date: 11 May 2026
  • Accept Date: 13 May 2026

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