A radial basis collocation method for pricing American options under regime-switching jump-diffusion models

The Markovian regime-switching paradigm has become one of the prevailing models in mathematical finance. It is now widely known that under the regime-switching model, the market is incomplete and so the option valuation problem in this framework will be a challenging task of considerable importance for market practitioners and academia. Our concern here is to solve the pricing problem for American options in a Markov-modulated jump-diffusion model, based on a meshfree approach using radial basis functions. In this respect, we solve a set of coupled partial integro-differential equations with the free boundary feature by expanding the solution vector in terms of radial basis functions and then collocating the resulting system of equations at some pre-specified points. This method exhibits a superlinear order of convergence in space and a linear order in time and also has an acceptable speed in comparison with some existing methods. We will compare our results with some recently proposed approaches. (c) 2012 IMACS. Published by Elsevier B.V. All rights reserved.