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

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.
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https://hal.archives-ouvertes.fr/hal-01686952
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Submitted on : Thursday, January 31, 2019 - 7:27:01 PM
Last modification on : Monday, February 21, 2022 - 8:08:02 AM
Long-term archiving on: : Wednesday, May 1, 2019 - 6:51:43 PM

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  • HAL Id : hal-01686952, version 3

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Ankush Agarwal, Stefano de Marco, Emmanuel Gobet, José López-Salas, Fanny Noubiagain, et al.. Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements. 2019. ⟨hal-01686952v3⟩

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