Finite DifferenceFourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-04
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We study the fractional Black–Scholes model (FBSM) of option pricing in the fractal transmission system.
In this work, we develop a full-discrete numerical scheme to investigate the dynamic behavior of FBSM.
The proposed scheme implements a known L1 formula for the α-order fractional derivative and Fourier-spectral method for the discretization of spatial direction.
Energy analysis indicates that the constructed discrete method is unconditionally stable.
Error estimate indicates that the 2−α-order formula in time and the spectral approximation in space is convergent with order OΔt2−α+N1−m, where m is the regularity of u and Δt and N are step size of time and degree, respectively.
Several numerical results are proposed to confirm the accuracy and stability of the numerical scheme.
At last, the present method is used to investigate the dynamic behavior of FBSM as well as the impact of different parameters.
American Psychological Association (APA)
He, Juan& Zhang, Aiqing. 2020. Finite DifferenceFourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1193193
Modern Language Association (MLA)
He, Juan& Zhang, Aiqing. Finite DifferenceFourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing. Mathematical Problems in Engineering No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1193193
American Medical Association (AMA)
He, Juan& Zhang, Aiqing. Finite DifferenceFourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1193193
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193193