The universal approximation theorem of artificial neural networks states that a forward feed network with a single hidden layer can approximate any continuous function, given a finite number of hidden units under mild constraints on the activation functions (see Hornik, 1991; Cybenko, 1989). Deep neural networks are preferred over shallow neural networks, as the later can be shown to require an exponentially larger number of hidden units (Telgarsky, 2016). This paper applies deep learning to train deep artificial neural networks to approximate derivative valuation functions using a basket option as an example. To do so it develops a Monte Carlo based sampling technique to derive appropriate training and test data sets. The paper explores a range of network geometries. The performance of the training phase and the inference phase are presented using GPU technology.
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