10.57647/ijm2c.2026.160101

A New Numerical Method for solving delay Black-Scholes model

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  • Mehrnoosh Abdous,
  • Alireza Vahidi*,
  • Tayebeh Damercheli,
  • Ommolbanin Sedaghatfar,

Received: 10-07-2025

Revised: 06-09-2025

Accepted: 20-09-2025

Published in Issue 31-03-2026

Published Online: 24-09-2025

Copyright (c) 2025 Mehrnoosh Abdous, Alireza Vahidi, Tayebeh Damercheli, Ommolbanin Sedaghatfar (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Abdous, M., Vahidi, A., Damercheli, T., & Sedaghatfar, O. (2026). A New Numerical Method for solving delay Black-Scholes model. International Journal of Mathematical Modelling & Computations. https://doi.org/10.57647/ijm2c.2026.160101
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Abstract

The objective of this study is to provide a numerical solution for stochastic delay differential equations, with a particular focus on the delay Black-Scholes model, utilizing the spectral collocation technique that employs radial basis functions. In this method, M-panels and r-point  Newton-Cotes integration was used to estimate the Ito integral. The main advantage of the proposed method is that it is easy to apply and leads to an algebraic equations system that is directly solved by numerical methods. Additionally, we analyze the stability and accuracy of the scheme through error estimation and comparisons with benchmark methods. To validate the approach, several numerical examples, including both linear and nonlinear SDDEs, are provided, demonstrating the method’s fast convergence and computational robustness. The results highlight the effectiveness of the spectral collocation approach in handling stochastic delays, offering a reliable framework for financial and engineering applications where randomness and delay play a critical role.

Keywords

  • Delay Black-Scholes model,
  • Spectral collocation technique,
  • Radial basis functions,
  • Newton-Cotes integration,
  • Ito integral
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