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Variance reduction methods for simulation of densities on Wiener space

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  • Arturo Kohatsu
  • Roger Pettersson
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    Abstract

    We develop a general error analysis framework for the Monte Carlo simulation of densities for functionals in Wiener space. We also study variance reduction methods with the help of Malliavin derivatives. For this, we give some general heuristic principles which are applied to diffusion processes. A comparison with kernel density estimates is made.

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    File URL: http://www.econ.upf.edu/docs/papers/downloads/597.pdf
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    Bibliographic Info

    Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 597.

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    Date of creation: Jan 2002
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    Handle: RePEc:upf:upfgen:597

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    Web page: http://www.econ.upf.edu/

    Related research

    Keywords: Stochastic differential equations; weak approximation; variance reduction; kernel density estimation;

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    Cited by:
    1. Kebaier, Ahmed & Kohatsu-Higa, Arturo, 2008. "An optimal control variance reduction method for density estimation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2143-2180, December.
    2. Talay, Denis & Zheng, Ziyu, 2004. "Approximation of quantiles of components of diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 23-46, January.
    3. Arturo Kohatsu & Montero Miquel, 2003. "Malliavin calculus in finance," Economics Working Papers 672, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Gobet, Emmanuel & Labart, CĂ©line, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
    5. Moez Mrad & Nizar Touzi & Amina Zeghal, 2006. "Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options," Computational Economics, Society for Computational Economics, vol. 27(4), pages 497-531, June.
    6. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    7. Guyon, Julien, 2006. "Euler scheme and tempered distributions," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 877-904, June.
    8. Nicola Cufaro Petroni & Piergiacomo Sabino, 2013. "Multidimensional quasi-Monte Carlo Malliavin Greeks," Decisions in Economics and Finance, Springer, vol. 36(2), pages 199-224, November.

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