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 yearsperiod. 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 frameworkof 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 .
This paper presents a framework of developing neural networks for predicting implied volatility surfaces. Conventional financial conditions and empirical evidence related to the implied volatility are incorporated into the neural network architecture design and model training including no static arbitrage, boundaries, asymptotic slope and volatility smile. They are also satisfied empirically by the option data on the S&P 500 index over twenty years. The developed neural network model and its simplified variations outperform the widely used surface stochastic volatility inspired (SSVI) model on the mean average percentage error in both in-sample and out-of-sample datasets. This study has two main methodological contributions. First, an accurate deep learning prediction model is developed and tailored to implied volatility surfaces. Second, a framework, which seamlessly combines data-driven models with financial theories , can be extended and applied to solve other related business problems .
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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 frameworkof integrating
This study has two main methodological contributions. First, an accurate deep learning prediction model is developed and tailored to implied volatility surfaces. Second, a framework, which seamlessly combines
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