  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.
