  We propose a neural network approach to price EU call options that
significantly outperforms some existing pricing models and comes with
guarantees that its predictions are economically reasonable. To achieve this,
we introduce a class of gated neural networks that automatically learn to
divide-and-conquer the problem space for robust and accurate pricing. We then
derive instantiations of these networks that are 'rational by design' in terms
of naturally encoding a valid call option surface that enforces no arbitrage
principles. This integration of human insight within data-driven learning
provides significantly better generalisation in pricing performance due to the
encoded inductive bias in the learning, guarantees sanity in the model's
predictions, and provides econometrically useful byproduct such as risk neutral
density.
