Efficient numerical simulation of fractional extended Heston models including interest rate driven by variable-order Brownian motions

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Ra.C., Islamic Azad University, Rasht, Iran.

2 Department of Mathematics, La.C., Islamic Azad University, Lahijan, Iran.

3 Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey.

Abstract

This research introduces an innovative and computationally efficient methodology for examining
fractional extended Heston models that incorporate interest rate within the framework of variable-order Brownian motions. The approach employs trapezoidal quadrature techniques to approximate both the fractional integral and the associated stochastic fractional systems, providing a robust numerical foundation. A comprehensive convergence analysis validates the proposed scheme’s mathematical soundness and reliability. The methodology’s accuracy and convergence characteristics are rigorously evaluated against established function integration methods from the existing literature, establishing its comparative advantages and limitations.
Building upon this theoretical framework, the developed approach is applied to solve these sophisticated models, revealing important insights into how stochastic effects influence stock price
dynamics. The investigation extends further to analyze crucial statistical indicators for determining
the optimal fractional order within the interval (0.5,1), using genetic algorithms. The research
also explores various parametric configurations of the variable-order Hurst index within the range
[0.5,1), providing deeper insights into the model’s behavior under different conditions. The results
show that the fractional Heston-Cox-Ingersoll-Ross model with time-varying Hurst index reduces
the all error criteria examined in this study compared to fixed Hurst models.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 29 October 2025

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History

  • Receive Date: 18 August 2025
  • Revise Date: 18 October 2025
  • Accept Date: 24 October 2025

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