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.
A neural network model that processes financial input data is developed to estimate the market price of options at closing. The network's ability to estimate closing prices is compared to the Black-Scholes model, the most widely used model for the pricing of options. Comparisons reveal that the mean squared error for the neural network is less than that of the Black-Scholes model in about half of the cases examined. The differences and similarities in the two modeling approaches are discussed. The neural network, which uses the same financial data as the Black-Scholes model, requires no distribution assumptions and learns the relationships between the financial input data and the option price from the historical data. The option-valuation equilibrium model of Black-Scholes determines option prices under the assumptions that prices follow a continuous time path and that the instantaneous volatility is nonstochastic.