Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation | Zendy

Sangkwon Kim | Zendy; Chaeyoung Lee | Zendy; Won Jin Lee | Zendy; Soobin Kwak | Zendy; Darae Jeong | Zendy; Junseok Kim | Zendy

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Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation

Author(s) -

Sangkwon Kim,

Chaeyoung Lee,

Won Jin Lee,

Soobin Kwak,

Darae Jeong,

Junseok Kim

Publication year - 2021

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 28

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2021/9984473

Subject(s) - black–scholes model , finite difference scheme , mathematics , scheme (mathematics) , finite difference , finite difference method , mathematical analysis , econometrics , volatility (finance)

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.

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