The Longstaff.Schwartz algorithm for Lévy models: Results on fast and slow convergence

We investigate the Longstaff.Schwartz algorithm for American option pricing assuming that both the number of regressors and the number of Monte Carlo paths tend to infinity. Our main results concern extensions, respectively, applications of results by Glasserman and Yu [Ann. Appl. Probab. 14 (2004) 2090.2119] and Stentoft [Manag. Sci. 50 (2004) 1193.1203] to several Lévy models, in particular the geometric Meixner model. A convenient setting to analyze this convergence problem is provided by the Lévy.Sheffer systems introduced by Schoutens and Teugels.