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arXiv · 2408.01185

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·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.

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A. Agarwal, S. De Marco, E. Gobet, J. G. Lopez-Salas, F. Noubiagain, A. Zhou. 2024-08-02. Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements. https://doi.org/10.1051/proc/201965001

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