  We show that the moment explosion time in the rough Heston model [El Euch,
Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the
classical Heston model. Upper and lower bounds for the explosion time are
established, as well as an algorithm to compute the explosion time (under some
restrictions). We show that the critical moments are finite for all maturities.
For negative correlation, we apply our algorithm for the moment explosion time
to compute the lower critical moment.
