Recent papers by Feng, Forde and Fouque (SIAM J Financial Math, 2010) and Feng, Fouque and Kumar (Ann. Appl. Prob, 2012) have obtained large deviation results for the small time asymptotic behavior for the log stock price in a fast mean-reverting stochastic volatility model. These results involve specific assumptions about the rate of growth of the speed parameter in the volatility process as the small time decreases to zero.