پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 856 |
| تعداد مقالات | 8,310 |
| تعداد مشاهده مقاله | 52,843,432 |
| تعداد دریافت فایل اصل مقاله | 9,270,235 |
An efficient numerical method based on cubic B--splines for the time--fractional Black--Scholes European option pricing model | ||
| Journal of Mathematical Modeling | ||
| مقاله 2، دوره 12، شماره 3، آذر 2024، صفحه 405-417 اصل مقاله (4.43 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.26551.2341 | ||
| نویسندگان | ||
| Hamed Payandehdoost Masouleh1؛ Mojgan Esmailzadeh* 2 | ||
| 1Department of Accounting, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran | ||
| 2Department of Applied Mathematics, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran | ||
| چکیده | ||
| In this study, we develop a precise and effective numerical approach to solve the time--fractional Black--Scholes equation, which is used to calculate European options. The method employs cubic B-spline collocation for spatial discretization and a finite difference method for time discretization. An analysis of the method's stability is conducted. Finally, two numerical examples are included to show the effectiveness and applicability of the suggested method. | ||
| کلیدواژهها | ||
| Cubic B-spline؛ time-fractional؛ Black-Scholes؛ European option pricing model | ||
| مراجع | ||
|
[1] J. Alavi, H. Aminikhah, An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation, Comput. Appl. Math. 42 (2023) 350. [2] H. Aminikhah, J. Alavi, An efficient B-spline difference method for solving system of nonlinear parabolic PDEs, SeMA Journal 75 (2018) 335–348. [3] S. Ampun, P. Sawangtong, The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative, Mathematics 9 (2021) 214. [4] P. Assari, S. Cuomo, The numerical solution of fractional differential equations using the Volterra integral equation method based on thin plate splines, Eng. Comput. 35 (2019) 1391–1408. [5] G. Changhong, F. Shaomei, H. Yong, Derivation and Application of Some Fractional BlackScholes Equations Driven by Fractional G-Brownian Motion, Comput. Econ. 61 (2023) 1681–1705. [6] K. Kazmi, A second order numerical method for the time-fractional BlackScholes European option pricing model, J. Comput. Appl. Math. 418 (2023) 114647. [7] M.N. Koleva, L.G. Vulkov, Numerical solution of time-fractional BlackScholes equation, Comp. Appl. Math. 36 (2017) 1699–1715. [8] F. Mirzaee, K. Sayevand, S. Rezaei, N. Samadyar, Finite Difference and Spline Approximation for Solving Fractional Stochastic Advection-Diffusion Equation, Iran J. Sci. Technol. Trans. Sci. 45 (2021) 607–617. [9] D. Prathumwan, K. Trachoo, On the solution of two-dimensional fractional Black-Scholes equation for Eu- ropean put option, Adv. Differ. Equ. 2020 (2020) 146. [10] S.R. Saratha, G.S. Sundara Krishnan, M. Bagyalakshmi, C.P. Lim, Solving BlackScholes equations using fractional generalized homotopy analysis method, Comp. Appl. Math. 39 (2020) 262. [11] M. She, L. Li, R. Tang, D.F. Li, A novel numerical scheme for a time fractional BlackScholes equation, J. Appl. Math. Comput. 66 (2021) 853–870. [12] M. Taghipour, H. Aminikhah, A spectral collocation method based on fractional Pell functions for solving timefractional BlackScholes option pricing model, Chaos Solit. Fractals 163 (2022) 112571. | ||
|
آمار تعداد مشاهده مقاله: 372 تعداد دریافت فایل اصل مقاله: 566 |
||