Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model

American put options with the regime-switching model is a system of coupled free boundary problems. In this study, we present an accurate finite difference method Hermite interpolation for solving system. To end, first employ logarithmic transformation to map each regime fixed interval and then eliminate first-order derivatives in transformed by taking obtain partial differential equations which call asset-delta-gamma-speed equations. We discretize using fourth-order compact scheme Crank–Nicholson method. At same time, influence other asset option sensitivities are estimated based on third-order interpolation. As such, overall consists four tridiagonal linear systems, can be easily solved Thomas algorithm Gauss–Seidel iteration. The obtained applied two, four, sixteen regimes, respectively. Our results show that provides solution fast computation as compared existing numerical methods.