Need to separate two different situations here: 1) where there are pretty complete markets for implied volatility, looking at the past matters less to little,

Need to separate two different situations here: 1) where there are pretty complete markets for implied volatility, looking at the past matters less to little, because there is a market for the "future volatility" you can hedge and interact with 2) when there isn't a good volatility market and hedging future volatility exposure is difficult, looking towards the past for some guidance increases in importance Both things can get complicated at times and in both cases it isn't strictly speaking the stddev you care about, but the quadratic variation (which can be the same under some assumptions).