The Annals of Applied Probability

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

Stefan Gerhold

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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.

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

First available in Project Euclid: 22 March 2011

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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]

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


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.

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