The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense
It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the pro...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
MDPI
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/79262 |
| _version_ | 1848764025267027968 |
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| author | Sawangtong, Panumart Trachoo, Kamonchat Sawangtong, Wannika Wiwatanapataphee, Benchawan |
| author_facet | Sawangtong, Panumart Trachoo, Kamonchat Sawangtong, Wannika Wiwatanapataphee, Benchawan |
| author_sort | Sawangtong, Panumart |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the proposed model is investigated by the Laplace transform homotopy perturbation method. |
| first_indexed | 2025-11-14T11:12:47Z |
| format | Journal Article |
| id | curtin-20.500.11937-79262 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:12:47Z |
| publishDate | 2018 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-792622020-08-19T06:56:34Z The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense Sawangtong, Panumart Trachoo, Kamonchat Sawangtong, Wannika Wiwatanapataphee, Benchawan Science & Technology Physical Sciences Mathematics Black-Scholes model fractional derivatives generalized Mittag-Leffer function Laplace transform homotopy perturbation method FINITE-DIFFERENCE METHOD AMERICAN OPTIONS MODEL It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the proposed model is investigated by the Laplace transform homotopy perturbation method. 2018 Journal Article http://hdl.handle.net/20.500.11937/79262 10.3390/math6080129 English http://creativecommons.org/licenses/by/4.0/ MDPI fulltext |
| spellingShingle | Science & Technology Physical Sciences Mathematics Black-Scholes model fractional derivatives generalized Mittag-Leffer function Laplace transform homotopy perturbation method FINITE-DIFFERENCE METHOD AMERICAN OPTIONS MODEL Sawangtong, Panumart Trachoo, Kamonchat Sawangtong, Wannika Wiwatanapataphee, Benchawan The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense |
| title | The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense |
| title_full | The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense |
| title_fullStr | The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense |
| title_full_unstemmed | The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense |
| title_short | The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense |
| title_sort | analytical solution for the black-scholes equation with two assets in the liouville-caputo fractional derivative sense |
| topic | Science & Technology Physical Sciences Mathematics Black-Scholes model fractional derivatives generalized Mittag-Leffer function Laplace transform homotopy perturbation method FINITE-DIFFERENCE METHOD AMERICAN OPTIONS MODEL |
| url | http://hdl.handle.net/20.500.11937/79262 |