The Longstaff--Schwartz algorithm for L\'{e}vy models: Results on fast and slow convergence

TL;DR

This paper analyzes the convergence behavior of the Longstaff--Schwartz algorithm for American option pricing within Lévy models, extending previous results to new models like the geometric Meixner, and examining conditions for fast and slow convergence.

Contribution

It extends convergence results of the Longstaff--Schwartz algorithm to Lévy models, including the geometric Meixner, using Lévy--Sheffer systems for analysis.

Findings

Results on convergence rates for Lévy models

Application to geometric Meixner model

Extension of previous theoretical frameworks

Abstract

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.