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Monte Carlo Greeks for financial products via approximative transition densities

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  • Joerg Kampen
  • Anastasia Kolodko
  • John Schoenmakers
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    Abstract

    In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. The results are applied in the context of a Libor market model.

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    File URL: http://arxiv.org/pdf/0807.1213
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0807.1213.

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    Date of creation: Jul 2008
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    Handle: RePEc:arx:papers:0807.1213

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    Web page: http://arxiv.org/

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    References

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    1. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(3), pages 271-286.
    2. Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, Springer, vol. 7(1), pages 1-27.
    3. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Asymptotic Properties of Monte Carlo Estimators of Derivatives," Management Science, INFORMS, INFORMS, vol. 51(11), pages 1657-1675, November.
    4. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance, EconWPA 0502005, EconWPA.
    5. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, Springer, vol. 10(1), pages 27-49, 01.
    6. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, Springer, vol. 1(4), pages 293-330.
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    Cited by:
    1. Denis Belomestny & G. Milstein & John Schoenmakers, 2010. "Sensitivities for Bermudan options by regression methods," Decisions in Economics and Finance, Springer, Springer, vol. 33(2), pages 117-138, November.

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