How to determine Historical Volatility best?

A

agrau

As many people often state, large parts of classical statistics can not be applied to security data, because these do not follow normal distribution.

I currently use Sheldon Natenberg's algorithm for historical volatility: The standard deviation of the logarithmic price changes measured at regular intervals of time, i.e. Std(Log(C/Ref(C,-1)), iPeriod)*Sqrt(250)*100 in Metastock language.

What would be a better algorithm to use? Any suggestions?

Thanks in advance,

Andreas
 
I heard that using log price scale is the transform that takes care of the problem of the fat tails. I passed statistics the second time I took it, the first time all I learned was a tremendous sympathy for the learning disabled.

There is a forum on Yahoo called Trading_Systems where people discuss this sort of thing. The moderator there is convinced that technical analysis has been proven to not work so the discussion steers towards arbitraging and statistics.

Max
 
I'm always amused that in Finance people give their name to very classical statistical formulas for I don't see what isn't classical in Sheldon Natenberg's "algorithm": the log transformation is very classical also since as soon as a distribution is not symetrical that's the first basic transformation one can do. As for the rest it is just the definition of the standard deviation of a sample i normalised for 250 days. In fact to be rigourous the formula should substract 1 to i (especially if i is small below 30) for there is one degree of liberty that has been consumed by the mean so as to calculate the variance. Sometimes people are not even rigorous when they mention 250 days whereas they should mention i for this is essentially what is needed to estimate the probability zone for mean and variance.

As for the answer to the question the problem is what you mean by best. As for myself I use this: for example 8550.96 is the "normal" high zone for this week (real high until today has been 8559). It is not based on definition only but also on probability law + my experience of the market. The coefficients for indices are universal that is to say I don't have to change for french market or for Dow Jones. I will explain in an article how to calculate it.

<IMG SRC=http://harrytrader.membres.jexiste.org/guide/galleries/harry/prob_zone.gif>

Quote from agrau:

As many people often state, large parts of classical statistics can not be applied to security data, because these do not follow normal distribution.

I currently use Sheldon Natenberg's algorithm for historical volatility: The standard deviation of the logarithmic price changes measured at regular intervals of time, i.e. Std(Log(C/Ref(C,-1)), iPeriod)*Sqrt(250)*100 in Metastock language.

What would be a better algorithm to use? Any suggestions?

Thanks in advance,

Andreas
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