  We consider the supervised learning problem of learning the price of an
option or the implied volatility given appropriate input data (model
parameters) and corresponding output data (option prices or implied
volatilities). The majority of articles in this literature considers a (plain)
feed forward neural network architecture in order to connect the neurons used
for learning the function mapping inputs to outputs. In this article, motivated
by methods in image classification and recent advances in machine learning
methods for PDEs, we investigate empirically whether and how the choice of
network architecture affects the accuracy and training time of a machine
learning algorithm. We find that for option pricing problems, where we focus on
the Black--Scholes and the Heston model, the generalized highway network
architecture outperforms all other variants, when considering the mean squared
error and the training time as criteria. Moreover, for the computation of the
implied volatility, after a necessary transformation, a variant of the DGM
architecture outperforms all other variants, when considering again the mean
squared error and the training time as criteria.
