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Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements

Author

Listed:
  • Ankush Agarwal

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Stefano de Marco

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Emmanuel Gobet

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • José G López-Salas

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Fanny Noubiagain

    (Département de Mathématiques [Le Mans] - UM - Le Mans Université)

  • Alexandre Zhou

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech)

Abstract

We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relatively general regularity assumptions on the coefficients. We show how such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) requires the members to deposit variation and initial margins to cover their exposure. In the case when the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to define the price as a solution of a MKABSDE. We provide several linear and non-linear simpler approximations, which we solve using different numerical (deterministic and Monte-Carlo) methods.

Suggested Citation

  • Ankush Agarwal & Stefano de Marco & Emmanuel Gobet & José G López-Salas & Fanny Noubiagain & Alexandre Zhou, 2019. "Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements," Post-Print hal-01686952, HAL.
    • Handle: RePEc:hal:journl:hal-01686952
    DOI: 10.1051/proc/201965001
    Note: View the original document on HAL open archive server: https://hal.science/hal-01686952v3
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    References listed on IDEAS

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