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Advanced Monte Carlo methods for barrier and related exotic options

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  • Emmanuel Gobet

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    (LJK - Laboratoire Jean Kuntzmann - CNRS : UMR5224 - Université Joseph Fourier - Grenoble I - Université Pierre Mendès-France - Grenoble II - Institut Polytechnique de Grenoble - Grenoble Institute of Technology)

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    Abstract

    In this work, we present advanced Monte Carlo techniques applied to the pricing of barrier options and other related exotic contracts. It covers in particular the Brownian bridge approaches, the barrier shifting techniques (BAST) and their extensions as well. We leverage the link between discrete and continuous monitoring to design efficient schemes, which can be applied to the Black-Scholes model but also to stochastic volatility or Merton's jump models. This is supported by theoretical results and numerical experiments.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/31/99/47/PDF/GobetBarrierHandbook.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00319947.

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    Date of creation: Dec 2009
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    Publication status: Published, Mathematical Modeling and Numerical Methods in Finance, Elsevier (Ed.), 2009, 497-528
    Handle: RePEc:hal:journl:hal-00319947

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00319947
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    1. Gobet, Emmanuel & Menozzi, Stéphane, 2004. "Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 201-223, August.
    2. L.C.G. Rogers & E.J. Stapleton, 1997. "Fast accurate binomial pricing," Finance and Stochastics, Springer, vol. 2(1), pages 3-17.
    3. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
    4. Phelim Boyle & Yisong Tian, 1998. "An explicit finite difference approach to the pricing of barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 17-43.
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    Cited by:
    1. Gobet, Emmanuel & Menozzi, Stéphane, 2010. "Stopped diffusion processes: Boundary corrections and overshoot," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 130-162, February.

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