  In this paper, we present a method for the accurate estimation of the
derivative (aka.~sensitivity) of expectations of functions involving an
indicator function by combining a stochastic algorithmic differentiation and a
regression.
  The method is an improvement of the approach presented in [Risk Magazine
April 2018].
  The finite difference approximation of a partial derivative of a Monte-Carlo
integral of a discontinuous function is known to exhibit a high Monte-Carlo
error. The issue is evident since the Monte-Carlo approximation of a
discontinuous function is just a finite sum of discontinuous functions and as
such, not even differentiable.
  The algorithmic differentiation of a discontinuous function is problematic. A
natural approach is to replace the discontinuity by continuous functions. This
is equivalent to replacing a path-wise automatic differentiation by a (local)
finite difference approximation.
  We present an improvement (in terms of variance reduction) by decoupling the
integration of the Dirac delta and the remaining conditional expectation and
estimating the two parts by separate regressions. For the algorithmic
differentiation, we derive an operator that can be injected seamlessly - with
minimal code changes - into the algorithm resulting in the exact result.
