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Adaptative Monte Carlo Method, A Variance Reduction Technique

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  • Arouna Bouhari

    (CERMICS, Ecole Nationale des Ponts et Chaussées, 77455 Marne La Vallée, 6 et 8 av. Blaise Pascal, France, email:)

Abstract

In this article we propose an adaptative variance reduction method for Monte Carlo simulations. The method uses importance sampling scheme based on a change of drift. The change of drift is selected adaptatively through the Monte Carlo computation by using a suitable sequence of approximation. We state and prove theoretical results supporting the use of the method. We develop two applications of the procedure for variance reduction in a Monte Carlo computation in finance and in reliability.

Suggested Citation

  • Arouna Bouhari, 2004. "Adaptative Monte Carlo Method, A Variance Reduction Technique," Monte Carlo Methods and Applications, De Gruyter, vol. 10(1), pages 1-24, March.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:1:p:1-24:n:1
    DOI: 10.1515/156939604323091180
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    References listed on IDEAS

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    1. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Citations

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    Cited by:

    1. Bernard Lapeyre & J'er^ome Lelong, 2010. "A framework for adaptive Monte-Carlo procedures," Papers 1001.3551, arXiv.org, revised Jul 2010.
    2. Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473, arXiv.org, revised Feb 2007.
    3. repec:hal:wpaper:hal-00842362 is not listed on IDEAS
    4. Laetitia Badouraly Kassim & J'er^ome Lelong & Imane Loumrhari, 2013. "Importance sampling for jump processes and applications to finance," Papers 1307.2218, arXiv.org.
    5. Olivier Aj Bardou & Noufel Frikha & G. Pag`es, 2008. "Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling," Papers 0812.3381, arXiv.org, revised Dec 2010.
    6. Laetitia Badouraly Kassim & Jérôme Lelong & Imane Loumrhari, 2015. "Importance sampling for jump processes and applications to finance," Post-Print hal-00842362, HAL.

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