• ISSN: 2010-023X (Print)
    • Abbreviated Title: Int. J. Trade, Economics and Financ.
    • Frequency: Quaterly
    • DOI: 10.18178/IJTEF
    • Editor-in-Chief: Prof.Tung-Zong (Donald) Chang
    • Managing Editor: Ms. Shira. W. Lu
    • Abstracting/ Indexing:  Crossref, CNKI, EBSCO
    • E-mail: ijtef.editorial.office@gmail.com
IJTEF 2022 Vol.13(2): 36-41 ISSN: 2010-023X
DOI: 10.18178/ijtef.2022.13.2.720

A Study on Analytical and Numerical Solutions of Three Types of Black-Scholes Models

Jiawei He

Abstract—In the history of option pricing, one of the most significant models is the Black-Scholes model. In this paper, the classical Black-Scholes model for European and American options and its two modified forms will be described, which are nonlinear Black-Scholes model and time-fractional BlackScholes model. The main purpose of this paper is to discuss those most popular analytical and numerical solutions for solving each type of Black-Scholes model. Among those solutions, common schemes will be summarized and the qualitative analysis of those methods, such as stability and convergence, will be presented.

Index Terms—Analytical solution, Black-Scholes model, nonlinear Black-Scholes model, numerical solution, timefractional Black-Scholes model.

Jiawei He is with the Graduate School of Arts and Sciences, Columbia University, New York, NY 10025, USA (e-mail: jh4006@columbia.edu).

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Cite: Jiawei He, "A Study on Analytical and Numerical Solutions of Three Types of Black-Scholes Models," International Journal of Trade, Economics and Finance vol.13, no.2, pp. 36-41, 2022.

Copyright © 2022 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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