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Optimal Delaunay and Voronoi Quantization Schemes for Pricing American Style Options

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Numerical Methods in Finance

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 12))

Abstract

We review in this article pure quantization methods for the pricing of multiple exercise options. These quantization methods have the common advantage, that they allow a straightforward implementation of the Backward Dynamic Programming Principle for optimal stopping and stochastic control problems. Moreover we present here for the first time a unified discussion of this topic for Voronoi and Delaunay quantization and illustrate the performances of both methods by several numerical examples.

MSC Code: 62L15, 60F25, 65C50, 65D32

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Acknowledgements

Parts of this work has benefited from helpful discussions with S. Bouthemy and N. Casini (GDF-SUEZ).

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Authors and Affiliations

  1. Laboratoire de Probabilitités & Modèles Aléatoires (LPMA), Université Pierre & Marie Curie (UPMC), case 188, 4 pl. Jussieu, 75252, Paris cedex 5, France

    Gilles Pagès & Benedikt Wilbertz

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  1. Gilles Pagès
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  2. Benedikt Wilbertz
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Correspondence to Gilles Pagès .

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Editors and Affiliations

  1. Dept. Operations Research &, Financial Engineering, Princeton University, Charlton Street, Princeton, 08544, New Jersey, USA

    René A. Carmona

  2. Centre INRIA Bordeaux Sud-Ouest, Institut de Mathématiques, Université Bordeaux I, Cours de la Libération 351, Talence Cedex, 33405, France

    Pierre Del Moral

  3. Centre INRIA Bordeaux Sud-Ouest, Institut de Mathématiques, Université Bordeaux I, cours de la Libération 351, Talence Cedex, 33405, France

    Peng Hu

  4. EDF Recherche et Développement, Avenue Générale de Gaulle 1, Clamart, 92140, France

    Nadia Oudjane

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Pagès, G., Wilbertz, B. (2012). Optimal Delaunay and Voronoi Quantization Schemes for Pricing American Style Options. In: Carmona, R., Del Moral, P., Hu, P., Oudjane, N. (eds) Numerical Methods in Finance. Springer Proceedings in Mathematics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25746-9_6

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