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Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative
المؤلفون المشاركون
Sene, Ndolane
Sène, Babacar
Ndiaye, Seydou Nourou
Traoré, Awa
المصدر
Discrete Dynamics in Nature and Society
العدد
المجلد 2020، العدد 2020 (31 ديسمبر/كانون الأول 2020)، ص ص. 1-11، 11ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2020-07-25
دولة النشر
مصر
عدد الصفحات
11
التخصصات الرئيسية
الملخص 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.
نمط استشهاد جمعية علماء النفس الأمريكية (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
نمط استشهاد الجمعية الأمريكية للغات الحديثة (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
نمط استشهاد الجمعية الطبية الأمريكية (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
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1153460
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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