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

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

2008-02-13

arxiv.org/abs/0802.1831v2

Annals of Applied Probability 2011, Vol. 21, No. 2, 589-608

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP704 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP704

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 L\'{e}vy models, in particular the geometric Meixner model. A convenient setting to analyze this convergence problem is provided by the L\'{e}vy--Sheffer systems introduced by Schoutens and Teugels.

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