Applying the Generalized Laplace Residual Power Series Method to the Time-Fractional Multi-Asset Black-Scholes European Option Pricing Model
2
Issued Date
2025-01-01
Resource Type
ISSN
27051064
eISSN
27051056
Scopus ID
2-s2.0-105009432454
Journal Title
Contemporary Mathematics Singapore
Volume
6
Issue
3
Start Page
3809
End Page
3831
Rights Holder(s)
SCOPUS
Bibliographic Citation
Contemporary Mathematics Singapore Vol.6 No.3 (2025) , 3809-3831
Suggested Citation
Sukwong N., Sawangtong W., Sitthiwirattham T., Sawangtong P. Applying the Generalized Laplace Residual Power Series Method to the Time-Fractional Multi-Asset Black-Scholes European Option Pricing Model. Contemporary Mathematics Singapore Vol.6 No.3 (2025) , 3809-3831. 3831. doi:10.37256/cm.6320257266 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/111120
Title
Applying the Generalized Laplace Residual Power Series Method to the Time-Fractional Multi-Asset Black-Scholes European Option Pricing Model
Corresponding Author(s)
Other Contributor(s)
Abstract
It is a well-known fact that the Black-Scholes model is used in order to analyse the behavior of the financial market with regard to the pricing of options. An explicit analytical solution to the Black-Scholes equation is known as the Black-Scholes formula. The Black-Scholes equation is modified by mathematicians in the form of fractional Black-Scholes equations. Unfortunately, there are certain cases in which the fractional-order Black-Scholes equation does not have a closed-form formula. This article demonstrates the method for deriving analytical solutions to the fractional multi-asset Black-Scholes equation with the left-side Caputo-type Katugampola fractional derivative. The<sup>tρ</sup>ρ<sup>-Laplace</sup> residual power series approach, which blends the residual power series method with the<sup>tρ</sup>-Laplace transform, is the ρ methodology used to find analytical solutions to this equation. The suggested method is remarkably precise and efficient for the fractional multi-asset Black-Scholes equation, according to numerical analyses. This confirms that the<sup>tρ</sup>ρ<sup>-Laplace</sup> residual power series method is among the most effective techniques for finding analytical solutions to fractional-order differential equations.