  We develop deep learning models to learn the hedge ratio for S&P500 index
options directly from options data. We compare different combinations of
features and show that a feedforward neural network model with time to
maturity, Black-Scholes delta and a sentiment variable (VIX for calls and index
return for puts) as input features performs the best in the out-of-sample test.
This model significantly outperforms the standard hedging practice that uses
the Black-Scholes delta and a recent data-driven model. Our results demonstrate
the importance of market sentiment for hedging efficiency, a factor previously
ignored in developing hedging strategies.
