Title: Pricing of European options through a jump-diffusion technique on market prices

Authors: Y. Esmaeelzade Aghdam; H. Mesgarani; A. Amin

Addresses: Department of Mathematics, Farhangian University, P.O. Box 14665-889, Tehran, Iran ' Department of Mathematics, Shahid Rajaee Teacher Training University, Tehran, Iran ' Department of Mathematics, Shahid Rajaee Teacher Training University, Tehran, Iran

Abstract: This paper provides an efficient approach for approximating the Black-Scholes (B-S) model with a market price jump spread term for European put and call options using orthogonal Gegenbauer polynomials (OGP) and time derivative estimation. Therefore, we formulate a genuine and speedy numerical calculation technique that is grounded on the established convergence recovery method. The derivative matrix of a OGP polynomial is obtained through this polynomial property. Using the numerical method has an advantage in speed and efficiency, as the orthogonality of OGP polynomials and operational matrices decreases calculation time. To validate the validity of the new procedure, it presents two problems and provides numerical analyses that explain its efficiency and accuracy.

Keywords: Black-Scholes model; jump term; Gegenbauer polynomials; convergence; stability.

DOI: 10.1504/IJCEE.2026.151014

International Journal of Computational Economics and Econometrics, 2026 Vol.16 No.1/2, pp.106 - 121

Received: 27 Jul 2024
Accepted: 22 Oct 2024
Published online: 08 Jan 2026 *

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