Numerical method for pricing American options under regime-switching jump-diffusion models

Abstract

Our concern in this paper is to solve the pricing problem for American options in a Markov-modulated jump-diffusion model, based on a cubic spline collocation method. In this respect, we solve a set of coupled partial integro-differential equations PIDEs with the free boundary feature by using the horizontal method of lines to discretize the temporal variable and the spatial variable by means of Crank-Nicolson scheme and a cubic spline collocation method, respectively. This method exhibits a second order of convergence in space, in time and also has an acceptable speed in comparison with some existing methods. We will compare our results with some recently proposed approaches.

Keywords: American Option, Regime-Switching, Crank-Nicolson scheme, Spline collocation, Free Boundary Value Problem.