Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation
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 o...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9984473 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563017351430144 |
|---|---|
| author | Sangkwon Kim Chaeyoung Lee Wonjin Lee Soobin Kwak Darae Jeong Junseok Kim |
| author_facet | Sangkwon Kim Chaeyoung Lee Wonjin Lee Soobin Kwak Darae Jeong Junseok Kim |
| author_sort | Sangkwon Kim |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-635058e10be14b82b91f1ff712934118 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-635058e10be14b82b91f1ff7129341182025-02-03T01:21:09ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/9984473Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes EquationSangkwon Kim0Chaeyoung Lee1Wonjin Lee2Soobin Kwak3Darae Jeong4Junseok Kim5Department of MathematicsDepartment of MathematicsDepartment of Financial EngineeringDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn 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.http://dx.doi.org/10.1155/2021/9984473 |
| spellingShingle | Sangkwon Kim Chaeyoung Lee Wonjin Lee Soobin Kwak Darae Jeong Junseok Kim Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation Journal of Function Spaces |
| title | Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation |
| title_full | Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation |
| title_fullStr | Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation |
| title_full_unstemmed | Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation |
| title_short | Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation |
| title_sort | nonuniform finite difference scheme for the three dimensional time fractional black scholes equation |
| url | http://dx.doi.org/10.1155/2021/9984473 |
| work_keys_str_mv | AT sangkwonkim nonuniformfinitedifferenceschemeforthethreedimensionaltimefractionalblackscholesequation AT chaeyounglee nonuniformfinitedifferenceschemeforthethreedimensionaltimefractionalblackscholesequation AT wonjinlee nonuniformfinitedifferenceschemeforthethreedimensionaltimefractionalblackscholesequation AT soobinkwak nonuniformfinitedifferenceschemeforthethreedimensionaltimefractionalblackscholesequation AT daraejeong nonuniformfinitedifferenceschemeforthethreedimensionaltimefractionalblackscholesequation AT junseokkim nonuniformfinitedifferenceschemeforthethreedimensionaltimefractionalblackscholesequation |