Automatic adjoint differentiation for special functions involving expectations

José Brito, Andrei Goloubentsev and Evgeny Goncharov

Abstract

In this paper we explain how to compute gradients of functions of the form G = ½∑^m_i=1(E_yi - C_i)², which often appear in the calibration of stochastic models, using automatic adjoint differentiation and parallelization. We expand on the work of Goloubentsev and Lakshtanov and give approaches that are faster and easier to implement. We also provide an implementation of our methods and apply the technique to calibrate European options.