I would like to calculate intraday tick volatility between a time interval A to B.
E.g. If I have the quote and trade ticks for an instrument between 2023-02-17 10:00:02 to 2023-02-17 14:30:00, would the volatility be the SD of tick by tick returns? Or would I have to resample the data to e.g. 1 min bins and then calculate the SD of these 1 min bin returns? Also, would it be better to use trade ticks, or the midprice of quote ticks? What is the correct way to annualize the calculated volatility (if required)?
Extending this, if calculating the historical (e.g. 10 days) intraday tick volatility during this period, would the calculation be to average the individual intraday tick volatilities for each of the 10 days? E.g. $$\frac{1}{10} * (TickVol(A,B)_{t-1} + ... + TickVol(A,B)_{t-10})$$
I'm not sure if this method is right but it is the only way I can think of now.
