Stochastic Algorithmic Differentiation of (Expectations of) Discontinuous Functions (Indicator Functions)

11/14/2018

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by   Christian P. Fries, et al.

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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, April 2018. The algorithmic differentiation is a path-wise method and the path-wise differentiation of discontinuous payoffs is problematic. A natural approach is to replace the path-wise automatic differentiation by a (local) finite difference approximation. We show that this local finite difference approximation can be re-interpreted as a linear regression with the simplest regression basis function (a single indicator). With this formulation, we then replace the regression by more accurate estimators.