Before revision:  The range of rates includes behaviours similar to exponential L\'evy models and fractional stochastic volatility models . As a by-product, we make a conjecture on the small-maturity forward smile asymptotics of stochastic volatility models, in exact agreement with the results by Jacquier and Roome for the Heston model .
After revision:  The range of rates includes behaviours similar to exponential L\'evy models and fractional stochastic volatility models .