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A Comparison of Monte Carlo, Lattice Rules and Other Low-Discrepancy Point Sets

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Monte-Carlo and Quasi-Monte Carlo Methods 1998

Abstract

We explore how lattice rules can reduce the variance of the estimators for simulation problems, in comparison with the Monte Carlo method. To do this, we compare these two methods on option valuation problems in finance, along with two types of (t, s)-sequences. We also look at the effect of combining variance reduction techniques with the preceding approaches. Our numerical results seem to indicate that lattice rules are less affected by the “curse of dimensionality” than the other types of quasi-Monte Carlo methods and provide more precise estimators than Monte Carlo does.

Research supported by NSERC-Canada and FCAR-Quéscholarships

Research supported by NSERC-Canada grants No. ODGP0110050 and SMF0169893

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Author information

Authors and Affiliations

  1. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville Montréal, H3C 3J7, Canada

    Christiane Lemieux & Pierre L’Ecuyer

Authors
  1. Christiane Lemieux
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  2. Pierre L’Ecuyer
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Editors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010, Vienna, Austria

    Harald Niederreiter

  2. Claremont Graduate University, 925 N. Dartmouth Avenue, 91711, Claremont, CA, USA

    Jerome Spanier

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Lemieux, C., L’Ecuyer, P. (2000). A Comparison of Monte Carlo, Lattice Rules and Other Low-Discrepancy Point Sets. In: Niederreiter, H., Spanier, J. (eds) Monte-Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59657-5_22

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  • DOI: https://doi.org/10.1007/978-3-642-59657-5_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66176-4

  • Online ISBN: 978-3-642-59657-5

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