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

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Listed:
  • A. Agarwal
  • S. De Marco
  • E. Gobet
  • J. G. Lopez-Salas
  • F. Noubiagain
  • A. Zhou

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

  • A. Agarwal & S. De Marco & E. Gobet & J. G. Lopez-Salas & F. Noubiagain & A. Zhou, 2024. "Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements," Papers 2408.01185, arXiv.org.
    • Handle: RePEc:arx:papers:2408.01185
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