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Least-Squares Monte Carlo for Backward SDEs

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Numerical Methods in Finance

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

Abstract

In this paper we first give a review of the least-squares Monte Carlo approach for approximating the solution of backward stochastic differential equations (BSDEs) first suggested by Gobet et al. (Ann Appl Probab., 15:2172–2202, 2005). We then propose the use of basis functions, which form a system of martingales, and explain how the least-squares Monte Carlo scheme can be simplified by exploiting the martingale property of the basis functions. We partially compare the convergence behavior of the original scheme and the scheme based on martingale basis functions, and provide several numerical examples related to option pricing problems under different interest rates for borrowing and investing.

AMS classification: 65C30, 65C05, 91G20, 91G60

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Acknowledgements

The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft under grant BE3933/3-1.

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Authors and Affiliations

  1. Department of Mathematics, Saarland University, Campus E 2 4, D-66123, Saarbrücken, Germany

    Christian Bender & Jessica Steiner

Authors
  1. Christian Bender
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  2. Jessica Steiner
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Corresponding author

Correspondence to Christian Bender .

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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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Bender, C., Steiner, J. (2012). Least-Squares Monte Carlo for Backward SDEs. 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_8

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