In this research work, an explicit Runge-Kutta-Fehlberg  time integration with a fourth-order compact finite difference scheme in space  is employed for solving the regime-switching pricing model. First , we recast the free boundary problem into a system of nonlinear partial differential equations with a multi-fixed domain. We further introduce a transformation based on the square root function with a fixed free boundary from which a high order analytical approximation is obtained for computing the derivative of the optimal exercise boundary in each regime. The high order analytical approximation is achieved by the method of extrapolation. As such, it enables us to employ fourth-order spatial discretization and an adaptive time integration with Dirichlet boundary conditions for obtaining the numerical solution of the asset option, option Greeks, and the optimal exercise boundary for each regime . In the set of equations, Hermite interpolation with Newton basis is used to estimate the coupled assets options and option Greeks . A numerical experiment is carried out with two- and four-regimes examples and results are compared with the existing methods. The results obtained from the numerical experiment show that the present method provides better performance in terms of computational speed and more accurate solutions with a large step size.
In this research work, an explicit Runge-Kutta-Fehlberg (RKF) time integration with a fourth-order compact finite difference scheme in space and a high order analytical approximation of the optimal exercise boundary is employed for solving the regime-switching pricing model. In detail , we recast the free boundary problem into a system of nonlinear partial differential equations with a multi-fixed domain. We then introduce a transformation based on the square root function with a Lipschitz character from which a high order analytical approximation is obtained to compute the derivative of the optimal exercise boundary in each regime. We further compute the boundary values, asset option, and the option Greeks for each regime using fourth-order spatial discretization and adaptive time integration. In particular, the coupled assets options and option Greeks are estimated using Hermite interpolation with Newton basis. Finally, a numerical experiment is carried out with two- and four-regimes examples and results are compared with the existing methods. The results obtained from the numerical experiment show that the present method provides better performance in terms of computational speed and more accurate solutions with a large step size.
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fixed free boundary
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The high order analytical approximation is achieved by the method of extrapolation. As such, it enables us to employ fourth-order spatial discretization and an adaptive time integration with Dirichlet boundary conditions for obtaining the numerical solution of the
We further compute the boundary values,
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option Greeks, and the optimal exercise boundary
and the option Greeks
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using fourth-order spatial discretization and adaptive time integration. In particular,
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