Which volatility measure would you use for intraday minute data?

Question

I have a very detailed dataset - for each minute I can see 3 best bid and ask prices with associated quantities. Which measure of volatility would you use in such dataset? Some volatility measures use only the close price; Garman-Klass uses Open, low, high and close; but here it is much more detailed.

Here I would like a number which tells me how volatile day it was. I am thinking about simple standard deviation of the mid-price for each day. Are there some better estimates? Sorry if the question is obvious - I am not an expert in finance. Thanks!

Answer 1

Standard deviation is typically computed on the return distribution, not the price itself. You should maybe :

• (1) backtest your strategy with a given initial equity
• (2) each time you place a market order, you cross the order book with the 3 prices and sizes you talked about. You can then compute the price all inclusive (i.e., including bid ask spread, order book layers, and potentially broker fees). This will be more precise than the mid price
• (3) compute the return of each minute
• (4) compute the standard deviation of the return distribution, and maybe annualize it by multiplying by $\sqrt{365}$

Ps: if you really want to compute the standard deviation on the price itself and make any prediction out of it, you need to make sure your prices are stationary, otherwise moments (i.e., mean, standard dev etc) do no hold in time and your estimate may be useless.