Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation. (24th December 2021)

• Record Type: Journal Article
• Authors: Kim, Sangkwon; Lee, Chaeyoung; Lee, Wonjin; Kwak, Soobin; Jeong, Darae; Kim, Junseok
• Other Names: Youssri Youssri Hassan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-12-24
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/9984473
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation. The operator splitting scheme is used to efficiently solve the 3D time-fractional BS equation. We use a nonuniform grid for pricing 3D options. We compute the three-asset cash-or-nothing European call option and investigate the effects of the fractional-order α in the time-fractional BS model. Numerical experiments demonstrate the efficiency and fastness of the proposed scheme.