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Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative
Joint Authors
Sene, Ndolane
Sène, Babacar
Ndiaye, Seydou Nourou
Traoré, Awa
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-25
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The value of an option plays an important role in finance.
In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option.
We propose both a numerical scheme and an analytical solution.
Recent studies in fractional calculus have included new fractional derivatives with exponential kernels and Mittag-Leffler kernels.
These derivatives have been found to be applicable in many real-world problems.
As fractional derivatives without nonsingular kernels, we use a Caputo–Fabrizio fractional derivative and a Mittag-Leffler fractional derivative.
Furthermore, we use the Adams–Bashforth numerical scheme and fractional integration to obtain the numerical scheme and the analytical solution, and we provide graphical representations to illustrate these methods.
The graphical representations prove that the Adams–Bashforth approach is helpful in getting the approximate solution for the fractional Black–Scholes equation.
Finally, we investigate the volatility of the proposed model and discuss the use of the model in finance.
We mainly notice in our results that the fractional-order derivative plays a regulator role in the diffusion process of the Black–Scholes equation.
American Psychological Association (APA)
Sene, Ndolane& Sène, Babacar& Ndiaye, Seydou Nourou& Traoré, Awa. 2020. Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1153460
Modern Language Association (MLA)
Sene, Ndolane…[et al.]. Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1153460
American Medical Association (AMA)
Sene, Ndolane& Sène, Babacar& Ndiaye, Seydou Nourou& Traoré, Awa. Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1153460
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153460