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

Sangkwon Kim, Chaeyoung Lee, Wonjin Lee, Soobin Kwak, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number9984473
JournalJournal of Function Spaces
Volume2021
DOIs
Publication statusPublished - 2021

ASJC Scopus subject areas

  • Analysis

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