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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for American Option Pricing

Workshop: Concluding Workshop

Time: Wed, December 03, 2008, 16:00-16:30

Speaker: Stefan Gerhold

Abstract

The Longstaff-Schwartz Algorithm has become the method of choice for pricing American derivative contracts in high-dimensional settings. It approximates value functions by regression on a prescribed set of basis functions. If the number of basis functions is increased, the number of Monte Carlo paths must grow, too, to ensure convergence. Glasserman and Yu (Ann. Appl. Prob. 2004) have quantified the relation between these two parameters in the case where the underlying process is (geometric) Brownian motion. We extend this analysis to several well-known Lévy processes, using martingale identities found by Schoutens.

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