A generalized integral equation formulation for pricing American options under regime-switching model

In this paper, we present a generalized and highly efficient integral equation formulation for the price of American put options under regime-switching model with a goal of improving computational efficiency in mind, particularly when the number of regimes is large. Our achieved high efficiency is based on a newly proved theorem, which facilitates the decoupling of a system with simultaneously coupled PDEs so that they can be solved recursively at the numerical solution stage. Such a high efficiency is also fueled further by that the integral equation approach being characterized with its excellent trade off between maximizing analytical tractability and minimizing numerical discretization. Upon providing some numerical examples to demonstrate the implementation of the new approach and its efficiency, we anticipate that the very same theorem can be used to reduce the computational burden if other numerical approaches are adopted, for this highly challenging nonlinear problem.