Correct Historical Volatility Formula?

Bard · 2019-11-19T14:43:48+00:00

Which is the correct formula (or approximation) for Daily, 30 Day Historical Volatility (HV)?: ivolatility uses the second formula: https://www.ivolatility.com/help/2.html#hv I found the first set of code on PRC. annualVol = 252 HVPeriod = 30 periods = 7// 1 = intraday chart 7 = daily chart Returns = log(close / close[1]) StdDev = std[HVPeriod](Returns) HVol = (StdDev * sqrt(annualVol / periods)) * 100 or: annualVol = 252 HVPeriod = 30 //periods = 7// 1 = intraday chart 7 = daily chart Returns = log(close / close[1]) StdDev = std[HVPeriod](Returns) HVol = StdDev * sqrt(annualVol) * 100 Also shouldn’t it be: Returns = log(close [HVPeriod] / close[HVPeriod-1]) because it’s the sample std deviation we’re calculating? Thanks, it’d be good to clear this up as I see it has been discussed in these forums.

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11/19/2019 at 3:43 PM #113130 quote
Bard
Participant

Master
Which is the correct formula (or approximation) for Daily, 30 Day Historical Volatility (HV)?:

ivolatility uses the second formula: https://www.ivolatility.com/help/2.html#hv

I found the first set of code on PRC.
```
annualVol = 252
HVPeriod = 30 
periods = 7// 1 = intraday chart 7 = daily chart
 
Returns = log(close / close[1])
StdDev = std[HVPeriod](Returns)
HVol = (StdDev * sqrt(annualVol / periods)) * 100
```
or:
```
annualVol = 252
HVPeriod = 30
//periods = 7// 1 = intraday chart 7 = daily chart

Returns = log(close / close[1])
StdDev = std[HVPeriod](Returns)
HVol = StdDev * sqrt(annualVol) * 100
```
Also shouldn’t it be:
```
Returns = log(close [HVPeriod] / close[HVPeriod-1])
```
because it’s the sample std deviation we’re calculating?

Thanks, it’d be good to clear this up as I see it has been discussed in these forums.
11/19/2019 at 4:01 PM #113131 quote

Nicolas
Keymaster

Legend

I don’t think so, because in this case, in real time, you are calculation a standard deviation offset HVPeriod in the past.

11/19/2019 at 4:43 PM #113133 quote

Bard
Participant

Master

“Offset?”

Why do ivolatility state for HV calculations: https://www.ivolatility.com/help/2.html#hv

Note: In denominator we use n-1 instead of n to receive unbiased estimate of general dispersion (a square of a standard deviation). This adjustment is essential if we estimate standard deviation on the basis of a small number of observations.

Same with this quant site in Step #1: https://www.macroption.com/historical-volatility-calculation/

So wouldn’t n-1 be more appropriate if we’re attempting to calculate small samples of 10, 30 and 30 day returns from 252 periods?

Also why is there a divide by “periods” in the first formula – what is that doing, is it needed?

Cheers!
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