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Payandehdoost Masouleh, Hamed, Esmailzadeh, Mojgan. (1405). Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2026.69373.3413
Hamed Payandehdoost Masouleh; Mojgan Esmailzadeh. "Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models". سامانه مدیریت نشریات علمی, , , 1405, -. doi: 10.22034/cmde.2026.69373.3413
Payandehdoost Masouleh, Hamed, Esmailzadeh, Mojgan. (1405). 'Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2026.69373.3413
Payandehdoost Masouleh, Hamed, Esmailzadeh, Mojgan. Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models. سامانه مدیریت نشریات علمی, 1405; (): -. doi: 10.22034/cmde.2026.69373.3413

Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 اردیبهشت 1405    اصل مقاله (1.62 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2026.69373.3413
نویسندگان
Hamed Payandehdoost Masouleh1؛ Mojgan Esmailzadeh* 2
1Department of Accounting, BaA.C., Islamic Azad University, Bandar Anzali, Iran.
2Department of Applied Mathematics, BaA.C., Islamic Azad University, Bandar Anzali, Iran.
چکیده
In this study, we examine the generalized distributed-order fractional Black-Scholes equation through two distinct numerical approaches. The temporal derivative is approximated using a scheme analogous to the classical L1 method, ensuring accuracy in capturing fractional dynamics. For the spatial discretization, we employ two finite difference techniques alongside a collocation method
based on Romanovski-Jacobi polynomials, which provides enhanced flexibility in handling complex boundary behaviors. The numerical experiments confirm the high accuracy and robustness of the proposed methods in solving financial models governed by fractional dynamics. Each approach exhibits distinct strengths:
the collocation method achieves superior accuracy, while the finite difference schemes offer greater computational efficiency. Moreover, the use of an implicit formulation guarantees numerical stability even with larger time steps, making the method particularly suitable for long-term financial simulations.
کلیدواژه‌ها
Generalized Fractional distributed–order derivatives؛ Black–Scholes model؛ Finite difference method؛ Romanovski-Jacobi polynomials؛ Collocation method
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