Gated deep neural networks for implied volatility surfaces.

In this paper, we propose a gated deep neural network model to predict implied volatility surfaces. Conventional financial conditions and empirical evidence related to the implied volatility are incorporated into the neural network architecture design and calibration including no static arbitrage, boundaries, asymptotic slope and volatility smile. They are also satisfied empirically by the option data on the S&P 500 over a ten years period. Our proposed model outperforms the widely used surface stochastic volatility inspired model on the mean average percentage error in both in-sample and out-of-sample datasets. The research of this study has a fundamental methodological contribution to the emerging trend of applying the state-of-the-art information technology into business studies as our model provides a framework of integrating data-driven machine learning algorithms with financial theories and this framework can be easily extended and applied to solve other problems in finance or other business fields.