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Optimal Transport Filtering with Particle Reweighing in Finance

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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

We propose an optimal transportation approach to price European options under the Stein-Stein stochastic volatility model by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct the flow to a rarely visited areas of the state space by using a particle method (a mutation and a reweighing mechanism). We demonstrate the efficiency of our approach on a simple example for which a closed form formula is available. This method shows lower variance and bias compared to other filtering schemes recently developed in the signal-processing literature, including particle filter techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:cesptp:hal-01581903
    Note: View the original document on HAL open archive server: https://hal.science/hal-01581903
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    References listed on IDEAS

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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
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    Cited by:

    1. Raphaël Douady & Shohruh Miryusupov, 2017. "Hamiltonian Flow Simulation of Rare Events," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01581894, HAL.

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