A semi-analytic valuation of American options under a two-state regime-switching economy

In this study, we develop a semi-analytic method to evaluate American options under a two-state regime-switching economy. The two free boundaries corresponding to the states divide the pricing domain into two regions: a common continuation region and a transition region. Non-linear partial differential equation (PDE) systems are derived under the Black-Scholes framework for each region. The Laplace transform method is used to solve the PDE systems. Equations for determining the optimal exercise prices are obtained analytically and solved numerically in the Laplace space. A numerical inversion technique is then used to obtain the free boundaries and the option prices in the original time space. The results of various examples show that our technique is efficient and accurate.