Annualizing Intraday Volatility with Overnight and Seasonal Effects
Summary
The discussion explains why scaling minute-level volatility by the square root of time may not make it directly comparable with volatility estimated from daily observations. It identifies two adjustments: account for volatility that occurs overnight, and account for systematic variation in volatility across the trading day. For US exchange-traded products, activity often follows a U-shaped pattern, with higher volatility near the open and close than around midday. Comparing minute observations from different times therefore requires adjusting for this intraday seasonality.
The answers also point to a modeling caveat: high-frequency volatility estimation can rely on stationarity assumptions about the price formation process. At very short horizons, price dynamics may not be diffusive; a Hawkes process is mentioned as one framework that is non-diffusive at small scales and becomes diffusive asymptotically. The discussion gives no specific estimator or worked comparison, so implementation choices and the accuracy of any annualized figure depend on the data and assumptions used.
Key ideas
- Minute volatility may need adjustment before it can be compared with daily volatility.
- Overnight price variation should be included when estimating full-day risk.
- Intraday seasonality can make volatility differ systematically by time of day.
- High-frequency estimates may rely on stationarity and diffusion assumptions that fail at short horizons.
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Full text
# How to annualize intra-day volatility on minute data?
# How to annualize intra-day volatility on minute data?
I am trying to convert minute based volatility into annualized volatility in such a way that both are comparable. $Vol_{min} * \sqrt(t)$ does not seam to get them into the same scale if I annualize using daily data of minute data. What are the adjustments I can do to make volatility calculated using intra-day data more comparable to volatility calculated using daily data.
## Answer by lehalle (score 8, accepted)
https://quant.stackexchange.com/a/3266
Let allow me to split your question in parts:
- How to estimate volatility using high frequency data, see this question https://quant.stackexchange.com/a/3264/2299 and note that it rely on a stationnarity assumption of your PFP (Price Formation Process).
- You will have to add the overnight volatility to the intraday one.
- You can question the diffusive nature of the PFP, the Hawkes process are a convenient answer since they are not diffusive at small scales and asymptotically diffusive at larger ones.
## Answer by Tal Fishman (score 11)
https://quant.stackexchange.com/a/2540
Intraday seasonality is a major factor in comparing volatility at different times of day. Most time series display significantly higher volatility in the morning EST than mid-day. For US exchange-traded products, volatility picks up again just before 4:00 PM EST. This is known as the u-shaped volatility pattern for exchange-traded products. A proper annualization, which puts minutely volatility at one time of day on the same scale as volatility at another time, would require that you take into account all the systematic variation in volatility as a function of time.
This effect is very well known and has been thoroughly researched and described in An Introduction to High Frequency Finance, an excellent textbook written by the Olsen group, which also sells analytics based on the research described in their book. Their chapters 5 and 6 deal explicitly with an approach to your issue.
FYI, this question is tangentially related to some previous questions, How to update an exponential moving average with missing values? and How to generate synthetic FX data for backtesting? This book is also on my favorite list of books to understand the math in quantitative finance.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.