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I'm new in quant math, I'm self-studying it. I have two question in exp. daily range topic.

  1. 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?

  1. 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?

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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.

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  • $\begingroup$ hi, thank you. how to combine? thats something i don' get. can oyu give me example? $\endgroup$
    – c.m.
    Commented May 26 at 8:03
  • $\begingroup$ If you have two independent estimates, and you regard both as equally useful, you just average them. Otherwise, to give each estimate the proper weight, you can use OLS regression. $\endgroup$
    – nbbo2
    Commented May 26 at 8:43
  • $\begingroup$ simple arithmetic avg or geometric? so i get the gkyz hv for each day, i calculate the avg hv of the last 7 days + i check the IV of the atm strike at the brokerage, and take the avg of the iv and 7 days avg hv? (annualized of course, divided by sqrt(252) ) or weight the differently by OLS? $\endgroup$
    – c.m.
    Commented May 26 at 8:48

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