  Simulation of rough volatility models involves discretization of stochastic
integrals where the integrand is a function of a (correlated) fractional
Brownian motion of Hurst index $H \in (0,1/2)$. We obtain results on the rate
of convergence for the weak error of such approximations, in the special cases
when either the integrand is the fBm itself, or the test function is cubic. Our
result states that the convergence is of order $(3H+ \frac{1}{2}) \wedge 1$ for
exact left-point discretization, and of order $H+\frac{1}{2}$ for the hybrid
scheme with well-chosen weights.
