Is it technically correct to say that kurtosis is the "volatility of volatility"? - Page 2

Perhaps it might make sense to talk about the "variance of the sample variance," but "variance of the variance" is, on its face, the kind of rank pseudo-mathematical gibberish one often finds in business forums, minor-league stadium parking lots, and other such seedy venues.

The variance of the variance is a perfectly valid concept. Take stock prices.

Day 1: 234 with 1% intraday variance
Day 2: 233 with 2% intraday variance
Day 3: 234 with 1% intraday variance

How much and in what way does the second number vary? "What is its variance? (i.e the variance of the variance)" is a perfectly valid question.

Unbunch your panties gentlemen, there are concepts to be understood and you need to relax to enjoy it.

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07-24-2017 , 07:38 PM

#27

Zeno

Le Misanthrope

Join Date: Sep 2002 Posts: 22,369

You must understand the formulaic (precise) first - to properly interpret the fluid. That's why Shakespeare is so great. And Paul Dirac.

And this is a precise context*. That's statistics. It's your own fault if you trip up over the parameters and terms and units and yap it up like a wench on the prowl.

*Note the thread title, Is it technically correct.............

Last edited by Zeno; 07-24-2017 at 07:46 PM. Reason: added *

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07-25-2017 , 12:31 AM

#28

PairTheBoard

Carpal \'Tunnel

Join Date: Dec 2003 Posts: 10,037

Quote:

Originally Posted by ToothSayer

We might notice the OP asks about "Volatility" rather than "Variance". I'm not aware of where the term "Volatility" is used other than in the stock market. They even have a Volatility Index that you can trade. I've never really understood how that Index is calculated but I know it shot through the roof during the '08 crisis.

PairTheBoard

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07-25-2017 , 12:38 AM

#29

PairTheBoard

Carpal \'Tunnel

Join Date: Dec 2003 Posts: 10,037

Quote:

Originally Posted by PairTheBoard

I think the Volatility Index is calculated based on prices of options. I know that in the Black Scholes Model for options the key parameter is Variance. If the market bids the price of options up high it is guessing that it's likely the future action of stocks will see wide price swings.

PairTheBoard

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07-25-2017 , 12:43 AM

#30

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Quote:

Originally Posted by Trolly McTrollson

Not all distributions have non-serially correlated data points. Clustering, stickiness, mean-reversion, regime-change, etc. are all observable phenomena. It is definitely the stuff of seediness and you are wise to avoid the dens of iniquities for they are where the denizens of strange mathmatics create massive inequities.

Of course, none of this has even the slightest thing to do with kurtosis. There is one guy named Kurto and he does have a sis, but he isn't particularly good at the relevant mathematics.

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07-25-2017 , 01:46 AM

#31

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Quote:

Originally Posted by PairTheBoard

Not quite the bit interesting, but CBOE also calculates a thing called the VVIX, which is the implied volatility of implied volatility (or shorter, the VIX of VIX) They fail to mention that VVIX is the same thing as kurtosis for some reason.

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07-25-2017 , 01:55 AM

#32

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Quote:

Originally Posted by ToothSayer

They are used to dealing with proper population distributions where observations are independent and brownian.

In case I haven't made it abundantly clear, none of this has anything to do with kurtosis. I guess it is technically correct to say that you can state the word "kurtosis" in the same sentence as "volatility of volatility," but that is the entire extent of the relationship.

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07-25-2017 , 07:53 AM

#33

Trolly McTrollson

Carpal \'Tunnel

Join Date: Oct 2010 Posts: 36,757

What about the mean of the mean of the distribution?

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07-25-2017 , 08:58 AM

#34

PairTheBoard

Carpal \'Tunnel

Join Date: Dec 2003 Posts: 10,037

Then there's the 90 day moving average.

PairTheBoard

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07-25-2017 , 09:23 AM

#35

ToothSayer

Carpal \'Tunnel

Join Date: Jul 2015 Posts: 13,237

Quote:

Originally Posted by BrianTheMick2

They are used to dealing with proper population distributions where observations are independent and brownian.

It's why academics get their ass handed to them in the markets (by non academics) and in business (often by people without even degrees). Put too many assumptions and too much precision on something, and you're only describing your (now worthless) model, not reality.

Quote:

In case I haven't made it abundantly clear, none of this has anything to do with kurtosis. I guess it is technically correct to say that you can state the word "kurtosis" in the same sentence as "volatility of volatility," but that is the entire extent of the relationship.

Technically, there is an equation that links kurtosis with the variance of the variance, so they are linked, in some way. Just not the way OP would like. I didn't post it out of kindness to the OP.

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