I have tried to calculate IV and log-moneyness (=log(S/K)) for different times to expiry (M = less than 1 month, Q = less than 1 quarter, S = less than 1/2 of an year, Y = less than 1 year, Y (+) = more than 1 year). Doing this I've plotted the IV-smile for Call-options:
Notice that the IV-smile seems to "sharpen" when options get close to expiry. It other words: Small changes in log-moneyness implies large changes in IV when the option is closer to expiry - but why is that?
Following @will's suggestion of dividing log-moneyness by sqrt(T) results in a very nice Volatility Smile. Would someone care to explain why this is the case?