A Legendre–Galerkin spectral method for option pricing under regime switching models
The aim of this paper is to investigate an efficient spectral method for pricing European call options under regime-switching models. The main characteristic of this model is to incorporate the change in behavior of the underlying assets depending on different market states. The option pricing probl...
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| Language: | English |
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Elsevier
2024-11-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S259003742400075X |
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| author | Abdelmajid Ezzine Abdellah Alla Nadia Raissi |
| author_facet | Abdelmajid Ezzine Abdellah Alla Nadia Raissi |
| author_sort | Abdelmajid Ezzine |
| collection | DOAJ |
| description | The aim of this paper is to investigate an efficient spectral method for pricing European call options under regime-switching models. The main characteristic of this model is to incorporate the change in behavior of the underlying assets depending on different market states. The option pricing problem is modeled as a system of coupled Black–Scholes PDEs. The spatial discretization of the problem is performed using the Legendre–Galerkin spectral method based on Fourier-like basis functions, while the temporal discretization is based on a Crank–Nicolson scheme. Furthermore, the stability and convergence analysis are carried out for both the semi-and fully discretization of the resulted coupled PDE system. Finally, numerical experiments are illustrated to demonstrate the practical application potential of the discussed approach and its efficiency in real world cases. |
| format | Article |
| id | doaj-art-dd21ba9dff1c438daff0a58ef8ad3e55 |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-dd21ba9dff1c438daff0a58ef8ad3e552025-08-20T02:49:35ZengElsevierResults in Applied Mathematics2590-03742024-11-012410050510.1016/j.rinam.2024.100505A Legendre–Galerkin spectral method for option pricing under regime switching modelsAbdelmajid Ezzine0Abdellah Alla1Nadia Raissi2Corresponding author.; LAMA Laboratory, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, MoroccoLAMA Laboratory, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, MoroccoLAMA Laboratory, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, MoroccoThe aim of this paper is to investigate an efficient spectral method for pricing European call options under regime-switching models. The main characteristic of this model is to incorporate the change in behavior of the underlying assets depending on different market states. The option pricing problem is modeled as a system of coupled Black–Scholes PDEs. The spatial discretization of the problem is performed using the Legendre–Galerkin spectral method based on Fourier-like basis functions, while the temporal discretization is based on a Crank–Nicolson scheme. Furthermore, the stability and convergence analysis are carried out for both the semi-and fully discretization of the resulted coupled PDE system. Finally, numerical experiments are illustrated to demonstrate the practical application potential of the discussed approach and its efficiency in real world cases.http://www.sciencedirect.com/science/article/pii/S259003742400075XLegendre–Galerkin spectral methodsPricing optionsBlack–Scholes modelRegime-switching modelEuropean optionsCoupled PDEs |
| spellingShingle | Abdelmajid Ezzine Abdellah Alla Nadia Raissi A Legendre–Galerkin spectral method for option pricing under regime switching models Results in Applied Mathematics Legendre–Galerkin spectral methods Pricing options Black–Scholes model Regime-switching model European options Coupled PDEs |
| title | A Legendre–Galerkin spectral method for option pricing under regime switching models |
| title_full | A Legendre–Galerkin spectral method for option pricing under regime switching models |
| title_fullStr | A Legendre–Galerkin spectral method for option pricing under regime switching models |
| title_full_unstemmed | A Legendre–Galerkin spectral method for option pricing under regime switching models |
| title_short | A Legendre–Galerkin spectral method for option pricing under regime switching models |
| title_sort | legendre galerkin spectral method for option pricing under regime switching models |
| topic | Legendre–Galerkin spectral methods Pricing options Black–Scholes model Regime-switching model European options Coupled PDEs |
| url | http://www.sciencedirect.com/science/article/pii/S259003742400075X |
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