  We discuss the pricing and hedging of volatility options in some rough
volatility models. First, we develop efficient Monte Carlo methods and
asymptotic approximations for computing option prices and hedge ratios in
models where log-volatility follows a Gaussian Volterra process. While
providing a good fit for European options, these models are unable to reproduce
the VIX option smile observed in the market, and are thus not suitable for VIX
products. To accommodate these, we introduce the class of modulated Volterra
processes, and show that they successfully capture the VIX smile.
