A Generalized Approach for Pricing American Options Under Regime-Switching Model

In this paper, we present a new approach with which American option price under a general regime-switching model with an arbitrary finite number of economic states can be efficiently computed without solving a system of $n$ differential equations simultaneously. Comparing with all the existing approaches, this approach has a distinguishing feature: a set of completely decoupled integral equations is numerically integrated for each economical state within a finite $n$-state economy. Such a high efficiency is achieved through a pre-analysis of the associated matrices and their eigenvalues without worrying if the duplicated roots of the these matrices are misidentified as simple roots due to round-off errors or there are actually two extremely closed simple roots inherently in the original system. Numerical examples are provided to demonstrate the implementation of the new approach and its efficiency