Estimating Intraday Volatility from Minute-Level Trading Data
Summary
The response recommends measuring volatility from returns rather than from the level of the mid-price. For a strategy-oriented estimate, it suggests simulating market orders against the available bid and ask levels and quantities, then incorporating spread, depth, and possible broker fees to estimate the prices actually paid or received. Returns can be computed at each minute, and their standard deviation can summarize realized variation over the day.
It also mentions annualizing a daily estimate using a square-root-of-time convention. The data described includes multiple book levels, which can help reflect trading costs more closely than a mid-price series alone. The answer is not a comparison of specialized realized-volatility estimators, and its annualization suggestion assumes an appropriate return process and calendar. Using price-level standard deviation for prediction additionally requires stationarity; otherwise its moments may not remain stable over time.
Key ideas
- Volatility is generally summarized from returns rather than raw price levels.
- Simulating orders through available book levels can include spread and depth in realized execution prices.
- Minute-by-minute returns can be used to estimate intraday standard deviation.
- Annualization by square-root-of-time scaling depends on assumptions about returns and the time convention.
- Price-level statistics may be unreliable for prediction when prices are nonstationary.
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Full text
# Which volatility measure would you use for intraday minute data?
# Which volatility measure would you use for intraday minute data?
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 by Jerem Lachkar (score 1, accepted)
https://quant.stackexchange.com/a/75506
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.