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.
Payandehdoost Masouleh, H. and Esmailzadeh, M. (2026). Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.69373.3413
MLA
Payandehdoost Masouleh, H. , and Esmailzadeh, M. . "Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.69373.3413
HARVARD
Payandehdoost Masouleh, H., Esmailzadeh, M. (2026). 'Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.69373.3413
CHICAGO
H. Payandehdoost Masouleh and M. Esmailzadeh, "Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.69373.3413
VANCOUVER
Payandehdoost Masouleh, H., Esmailzadeh, M. Efficient Numerical Algorithms for Pricing Complex Financial Derivatives in Fractional Black-Scholes Models. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.69373.3413
)