Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step

Abstract

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.