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

• Published in: Applied numerical mathematics 2013-03, Vol.65, p.79-90
• Main Authors: Foroush Bastani, Ali, Ahmadi, Zaniar, Damircheli, Davood
• Format: Article
• Language: English
• Subjects: American option pricing; Coupled partial integro-differential equations (PIDEs); Jump-diffusion process; Lévy models; Radial basis functions; Regime switching
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2012.10.005

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.