3 years ago

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

Christian P. Fries

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.

Publisher URL: http://arxiv.org/abs/1811.05741

DOI: arXiv:1811.05741v1

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