We employ neural networks to understand volatility surface movements. We first use daily data on options on the S&P 500 index to derive a relationship between the expected change in implied volatility and three variables: the return on the index, the moneyness of the option, and the remaining life of the option. This model provides an improvement of 10.72% compared with a simpler analytic model. We then enhance the model with an additional feature: the level of the VIX index prior to the return being observed. This produces a further improvement of 62.12% and shows that the expected response of the volatility surface to movements in the index is quite different in high and low volatility environments.
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