  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.
