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

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  • Y. Esmaeelzade Aghdam
  • H. Mesgarani
  • A. Amin

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.

Suggested Citation

  • Y. Esmaeelzade Aghdam & H. Mesgarani & A. Amin, 2026. "Pricing of European options through a jump-diffusion technique on market prices," International Journal of Computational Economics and Econometrics, Inderscience Enterprises Ltd, vol. 16(1/2), pages 106-121.
    • Handle: RePEc:ids:ijcome:v:16:y:2026:i:1/2:p:106-121
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