Correct Historical Volatility Formula?

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

  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.

  HV

  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

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  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:

  HV

  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

  1 2 3 4 5 6 7

  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:

  Samp0le Std Dev

  Returns = log(close [HVPeriod] / close[HVPeriod-1])

  1	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.

  

  Bard

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  11/19/2019 at 4:01 PM #113131
  Nicolas

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

  

  Nicolas

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

  “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!

  

  Bard

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