Machine learning for option pricing: an empirical investigation of network architectures

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.