Predicting volatility is a critical activity for taking risk- adjusted decisions in asset trading and allocation. In order to provide effective decision-making support, in this paper we investigate the profitability of a deep Long Short-Term Memory (LSTM) Neural Network for forecasting daily stock market volatility using a panel of 28 assets representative of the Dow Jones Industrial Average index combined with the market factor proxied by the SPY and, separately, a panel of 92 assets belonging to the NASDAQ 100 index. The Dow Jones plus SPY data are from January 2002 to August 2008, while the NASDAQ 100 is from December 2012 to November 2017. If, on the one hand, we expect that this evolutionary behavior can be effectively captured adaptively through the use of Artificial Intelligence (AI) flexible methods, on the other, in this setting, standard parametric approaches could fail to provide optimal predictions. We compared the volatility forecasts generated by the LSTM approach to those obtained through use of widely recognized benchmarks models in this field, in particular, univariate parametric models such as the Realized Generalized Autoregressive Conditionally Heteroskedastic (R-GARCH) and the Glosten–Jagannathan–Runkle Multiplicative Error Models (GJR-MEM). The results demonstrate the superiority of the LSTM over the widely popular R-GARCH and GJR-MEM univariate parametric methods, when forecasting in condition of high volatility, while still producing comparable predictions for more tranquil periods.