Estimating SPX Daily Ranges from Volatility and OHLC Data
Summary
The post asks how to estimate an expected daily range for the S&P 500 and how a cited study may have calculated realized daily ranges. The questioner proposes using historical OHLC data to estimate volatility with the Garman-Klass-Yang-Zhang approach, averaging recent observations, and combining that estimate with at-the-money implied volatility. It also compares several range or volatility estimators against two reported daily figures, but does not establish which calculation produced them.
The reply recommends combining a trailing average of historical volatility with current at-the-money implied volatility and suggests Rogers-Satchell as a possible source of the study's realized-return figures. This is a tentative suggestion rather than a derivation: the excerpt supplies no formula details, validation, or comparison showing that Rogers-Satchell reproduces the reported values. It therefore offers a useful direction for investigation, but not a verified estimator or a demonstrated forecasting method.
Key ideas
- Historical OHLC prices can be used to estimate realized volatility.
- A trailing average of historical volatility may be considered alongside current at-the-money implied volatility when estimating a range.
- The reply proposes Rogers-Satchell as a possible explanation for the study's reported realized figures.
- The excerpt does not verify that estimator against the cited figures or establish forecasting accuracy.
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Full text
# Expected daily range (SPX) and daily realized range
# Expected daily range (SPX) and daily realized range
I'm new in quant math, I'm self-studying it. I have two question in exp. daily range topic.
- How can we make the possibly most accurate estimation for expected daily ranges?
My idea was to take data from yahoo finance, calculate realized vol using garman-klass-yang-zhang formula, then use a model (dunno which one) to calculate an expected trailing seven days avg historical vol for SPX. After that just get the ATM IV and use them both to get daily range. I'm using excel. Is there a way to do that?
- I've read somewhere months ago a research where a quant scrutinized the VIX performance comparing the VIX projected daily ranges (using $\text{VIX opening lvl} \times \sqrt\frac{1}{252} \cdot \sqrt\frac{2}{pi}$ formula) then calculated the daily realized ranges (I don't know the formula, that's what I wanna get). The data was:
(SPX on 3th of January 2022) open $4778.14$; high $4796.64$; low $4796.17$ and close $4796.56$ (previous close was at $4766.19$), and the research paper got 0.00844149 as daily realized return.
The next day OHLC data was $4804.51$, $4818.62$, $4774.27$, $4793.53$, and they got $0.009251912$ as daily realized return, 4th January 2022)
Trying to get how the research came up with that numbers I tried different methods: Parkinson took me to 0.004836038; Garman-Klass to $0.006175798$ and RS to $0.005806917$ if I put it in well. Yang Zhang also took me to $0.005742242$ however I'm not sure if I put in the formula correctly.
The closest numbers I got by $\ln\left(\frac{\text{high}}{\text{low}}\right)$ but not exactly the same. With VIX I got the same values the paper said using the formula.
Anyone have any clue what the calculation could have been? I'm not sure in mine, are those numbers correct if you check the data?
## Answer by BigMistake (score 0)
https://quant.stackexchange.com/a/79501
Try using historical volatility (calculated with the Garman-Klass-Yang-Zhang formula) and implied volatility. Calculate a trailing 7-day average of historical volatility and combine with current ATM implied volatility to estimate the expected range.
The research likely used the Rogers-Satchell estimator to calculate daily realized returns.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.