Pricing of European options through a jump-diffusion technique on market prices
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.
Fields of Study & Subjects
Stochastic processes and financial applications
Diffusion and Search Dynamics
Capital Investment and Risk Analysis
Publication details
- Journal / source
- International Journal of Computational Economics and Econometrics
- Volume
- 16
- Issue
- 1/2
- Pages
- 106–121
- Publication date
- 1 January 2026
- Language
- EN