Agarwal, A.De Marco, S.Gobet, EmmanuelLópez-Salas, José GermánNoubiagain, F.Zhou, A.2024-07-192024-07-192019-04-02A. Agarwal, S. De Marco, E. Gobet, J. G. López-Salas, F. Noubiagain, y A. Zhou, «Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements», ESAIM: ProcS, vol. 65, pp. 1-26, 2019, doi: 10.1051/proc/201965001.2267-3059http://hdl.handle.net/2183/38164The conference: July 17 - August 25, CIRM, Marseille[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.engAtribución 3.0 Españahttp://creativecommons.org/licenses/by/3.0/es/Non-linear pricingCVaR initial marginsAnticipative BSDEWeak non-linearityconference outputopen access10.1051/proc/201965001