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

A. Agarwal, S. De Marco, E. Gobet, J. G. Lopez-Salas, F. Noubiagain and A. Zhou

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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.

Date: 2024-08
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Published in Agarwal, A. et. al., Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements, ESAIM: ProcS, 2019, 65, 1-26

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