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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Main Authors: Abdelmajid Ezzine, Abdellah Alla, Nadia Raissi
Format: Article
Language:English
Published: Elsevier 2024-11-01
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.
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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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