am doing some work comparing Close to close vol vs Parkinsons vol estimator (which uses High Low) . As a base the first intuition I have without going into the formulae is that High low vol cannot be lesser than Close to close vol, But when I use the Parkinsons formula I can see that there are period whereby the High low vol (Parkinsons) is lesser than the close to close vol ...Could someone provide me with an intuition as to how this can be possible..I have read through the other thrreads talking about this topic but none of them touch upon my question raised above.would appreciate your help

I would have thought that if a stock jumps and stays at that level for the rest of the day, then the High-Low for that day is zero, as the stock has not moved at all from the open; whereas the close to close change, is the value of the jump. So when you calculate the vol using high to low you could get a lower number than using close to close.

Perhaps you are using the "raw" high/Low on the day whereas maybe you should adjust the high / low with the last closing price in order to incorporate the gap between the last close and the open. That's the only reason I can think about for a higher close-to-close realised relative to the high low?

The Parkinson and the Close-to-close are two different estimators of the same quantity (the vol of the Geometric Brownian motion). There is no reason why the Parkinson should always give a higher estimate; where is this written?!On the contrary if one of the estimators was always higher than the other, one of them would have to be wrong (biased).

Thanks chaps. all your comments appreciated.