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

Ankush Agarwal (), Stefano de Marco, Emmanuel Gobet (), José López-Salas, Fanny Noubiagain and Alexandre Zhou
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Ankush Agarwal: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Stefano de Marco: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
José López-Salas: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - 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 nationale des ponts et chaussées

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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.

Keywords: non-linear pricing; CVaR initial margins; anticipative BSDE; weak non-linearity (search for similar items in EconPapers)
Date: 2019-04-02
Note: View the original document on HAL open archive server: https://hal.science/hal-01686952v3
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Published in ESAIM: Proceedings and Surveys, 2019, 65, pp.1-26. ⟨10.1051/proc/201965001⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01686952

DOI: 10.1051/proc/201965001

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