Comput Econ (2014) 43:463–483 DOI 10.1007/s10614-013-9361-3 A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method K. Zhang · K. L. Teo · M. Swartz Accepted: 21 February 2013 / Published online: 6 March 2013 © Springer Science+Business Media New York 2013 Abstract This paper is devoted to develop a robust numerical method to solve a system of complementarity problems arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differential equations (PDEs). We then introduce a fitted finite volume method for the spatial discretization along with a fully implicit time stepping scheme for the PDEs, which results in a system of nonlinear algebraic equations. We show that this scheme is consistent, stable and monotone, hence convergent. To solve the system of nonlinear equations effectively, an iterative solution method is established. The convergence of the solution method is shown. Numerical tests are performed to examine the convergence rate and verify the effectiveness and robustness of the new numerical scheme. Keywords American option pricing · Regime switching · Penalty method · Finite volume method 1 Introduction Since Buffington and Elliott’s seminal paper (Buffington and Elliott 2002), the regime switching model has attracted much attention in option pricing theory. Unlike the standard Black–Scholesmodel (Black and Scholes 1973), the rationale behind the K. Zhang (B ) Business School, Shenzhen University, Shenzhen 518060, Guandong Province, China e-mail: mazhangkai@gmail.com K. L. Teo Department of Mathematics and Statistics, The Curtin University of Technology, Perth, WA, Australia M. Swartz Marshall School of Business, University of Southern California, Los Angeles, CA 90404, USA 123