  In this paper we develop a novel neural network model for predicting implied
volatility surface. Prior financial domain knowledge is taken into account. A
new activation function that incorporates volatility smile is proposed, which
is used for the hidden nodes that process the underlying asset price. In
addition, financial conditions, such as the absence of arbitrage, the
boundaries and the asymptotic slope, are embedded into the loss function. This
is one of the very first studies which discuss a methodological framework that
incorporates prior financial domain knowledge into neural network architecture
design and model training. The proposed model outperforms the benchmarked
models with the option data on the S&P 500 index over 20 years. More
importantly, the domain knowledge is satisfied empirically, showing the model
is consistent with the existing financial theories and conditions related to
implied volatility surface.
