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Hamiltonian Flow Simulation of Rare Events

Author

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  • Raphaël Douady

    (CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Shohruh Miryusupov

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Hamiltonian Flow Monte Carlo(HFMC) methods have been implemented in engineering, biology and chemistry. HFMC makes large gradient based steps to rapidly explore the state space. The application of the Hamiltonian dynamics allows to estimate rare events and sample from target distributions defined as the change of measures. The estimates demonstrated a variance reduction of the presented algorithm and its efficiency with respect to a standard Monte Carlo and interacting particle based system(IPS). We tested the algorithm on the case of the barrier option pricing.

Suggested Citation

  • Raphaël Douady & Shohruh Miryusupov, 2017. "Hamiltonian Flow Simulation of Rare Events," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01581894, HAL.
    • Handle: RePEc:hal:cesptp:hal-01581894
    Note: View the original document on HAL open archive server: https://hal.science/hal-01581894
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    References listed on IDEAS

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    1. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    2. Raphaël Douady & Shohruh Miryusupov, 2017. "Optimal Transport Filtering with Particle Reweighing in Finance," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01581903, HAL.
    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, October.
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