  We study neural networks as nonparametric estimation tools for the hedging of
options. To this end, we design a network, named HedgeNet, that directly
outputs a hedging strategy. This network is trained to minimise the hedging
error instead of the pricing error. Applied to end-of-day and tick prices of
S&P 500 and Euro Stoxx 50 options, the network is able to reduce the mean
squared hedging error of the Black-Scholes benchmark significantly. However, a
similar benefit arises by simple linear regressions that incorporate the
leverage effect.
