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 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.