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Efficient numerical simulation of fractional extended Heston models including interest rate driven by variable-order Brownian motions | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 آبان 1404 اصل مقاله (1.84 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.68717.3348 | ||
| نویسندگان | ||
| Zahra Tokasi1؛ Mousa Ilie* 1؛ Behrouz Parsa Moghaddam2؛ Kamyar Hosseini3 | ||
| 1Department of Mathematics, Ra.C., Islamic Azad University, Rasht, Iran. | ||
| 2Department of Mathematics, La.C., Islamic Azad University, Lahijan, Iran. | ||
| 3Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fractional calculus؛ Fractional extended Heston model؛ Fractional Brownian motion؛ Trapezoidal quadrature | ||
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آمار تعداد مشاهده مقاله: 166 تعداد دریافت فایل اصل مقاله: 287 |
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