Comparing volatility of a specific period between days

Question

I have 1 minute trade data for a particular stock and was wondering how I can compare the volatility of a particular period (08:00 - 09:00 for example) between days. I have data for 100 days and want to sort the days by most to least volatile.

My initial idea was to take the logarithm of each data point (close - open) and then just take the standard deviation of each day and sort by the outcome. This was after reading the following: "volatility is the standard deviation of the instrument's logarithmic returns". Seems a bit sketchy or maybe I am on the right track?

Thanks!

Answer 1

This question is perhaps a bit too simple for this forum. You are just asking how to compute volatility.

For every day do the following. Take the closing prices at 1 minute intervals for the time period 08:00 to 09:00 . That is a vector of 61 numbers: $$\{c_1,c_2,\cdots, c_{61}\}$$

Take the logarithms of these numbers: $$\{\ln c_1,\ln c_2,\cdots, \ln c_{61}\}$$

Now take the first differences of these values (that is 60 numbers): $$\{ \ln c_2-\ln c_1, \ln c_3-\ln c_2,\cdots, \ln c_{61}-\ln c_{60}\}$$

Finally take the standard deviation of these numbers. That is the volatility, expressed in "per minute" units.

(However, you should be aware that by taking readings so close together (every minute) you are measuring not only the volatility of the underlying stock but also "microstructure noise" that arises from the trading process, for example the effect of the bid ask bounce. This means that this reading of volatility will be somewhat inflated compared to lower frequency readings. Whether this matter or not for your application I do not know.).