The Annals of Applied Probability

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

Stefan Gerhold

Full-text: Open access

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 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.

Article information

Source
Ann. Appl. Probab. Volume 21, Number 2 (2011), 589-608.

Dates
First available in Project Euclid: 22 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1300800982

Digital Object Identifier
doi:10.1214/10-AAP704

Mathematical Reviews number (MathSciNet)
MR2807967

Zentralblatt MATH identifier
1219.62161

Subjects
Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Keywords
Option pricing dynamic programming Monte Carlo regression orthogonal polynomials Lévy–Meixner systems

Citation

Gerhold, Stefan. The Longstaff–Schwartz algorithm for Lévy models: Results on fast and slow convergence. Ann. Appl. Probab. 21 (2011), no. 2, 589--608. doi:10.1214/10-AAP704. https://projecteuclid.org/euclid.aoap/1300800982


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References

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