  Rough volatility models are known to reproduce the behavior of historical
volatility data while at the same time fitting the volatility surface
remarkably well, with very few parameters. However, managing the risks of
derivatives under rough volatility can be intricate since the dynamics involve
fractional Brownian motion. We show in this paper that surprisingly enough,
explicit hedging strategies can be obtained in the case of rough Heston models.
The replicating portfolios contain the underlying asset and the forward
variance curve, and lead to perfect hedging (at least theoretically). From a
probabilistic point of view, our study enables us to disentangle the
infinite-dimensional Markovian structure associated to rough volatility models.
