  In stochastic Volterra rough volatility models, the volatility follows a
truncated Brownian semi-stationary process with stochastic vol-of-vol.
Recently, efficient VIX pricing Monte Carlo methods have been proposed for the
case where the vol-of-vol is Markovian and independent of the volatility.
Following recent empirical data, we discuss the VIX option pricing problem for
a generalized framework of these models, where the vol-of-vol may depend on the
volatility and/or not be Markovian. In such a setting, the aforementioned Monte
Carlo methods are not valid. Moreover, the classical least squares Monte Carlo
faces exponentially increasing complexity with the number of grid time steps,
whilst the nested Monte Carlo method requires a prohibitive number of
simulations. By exploring the infinite dimensional Markovian representation of
these models, we device a scalable least squares Monte Carlo for VIX option
pricing. We apply our method firstly under the independence assumption for
benchmarks, and then to the generalized framework. We also discuss the rough
vol-of-vol setting, where Markovianity of the vol-of-vol is not present. We
present simulations and benchmarks to establish the efficiency of our method.
