[R-SIG-Finance] A question on volatility

Patrick Burns patrick at burns-stat.com
Wed Oct 5 22:39:07 CEST 2011


Paul,

If my understanding of Megh's question is correct,
then you've misinterpreted it.  I think the
correlations that are being sought are the correlations
between the volatilities of the assets, not the
correlations of the asset returns.

In any case, I'll attempt to give a bit of an answer
to the question as I understand it.

I'm uneasy about correlation of volatilities because
they are quite skewed.  Certainly favor rank correlations
over Pearson correlation.

Somewhere in Engle's body of work is a paper (or more)
on the transmission of volatility.  I don't recall
at all what the technique was, and vaguely remember
it being a mildly satisfying answer.

On 05/10/2011 21:10, Paul Ringseth wrote:
> Hi:
>
> You really need to jointly estimate the correlations with the variances.  The easiest technique (but not the best) is Orthogonal GARCH from Carl Alexander's papers (http://www.carolalexander.org/publish/download/DiscussionPapers/OrthogonalGARCH_Primer.pdf ).  Recently Engle has recommended a factor DCC-GARCH variant using a heuristic, he calls the MacGyver technique, for large covariance matrices (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1293628 ).    Then Engle, Shephard and Sheppard came up with an exceptionally interesting technique for fitting all parameters in any large covariance matrix http://www.economics.ox.ac.uk/Research/wp/pdf/paper403.pdf -- the estimator is essentially the sum of the quasi-MLE's of all pairs.  Also you should check out Engle's new book -- Anticipating Correlations ( http://press.princeton.edu/titles/8768.html ).
>
> Whatever you end up doing, you should backtest and compare to published results, for example at Engle's volatility lab -- http://vlab.stern.nyu.edu/analysis .
>
> But as long as the dimensionality of the desired correlation / covariance matrix is not too large (<= 16 should be ok ), a straightforward DCC-GARCH fit should work.  Here's some R code:
>
> http://www.r-project.org/conferences/useR-2008/slides/Nakatani.pdf
>
> Cheers -- Paul
>
> -----Original Message-----
> From: r-sig-finance-bounces at r-project.org [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of Megh Dal
> Sent: Wednesday, October 05, 2011 12:15 PM
> To: r-sig-finance at stat.math.ethz.ch
> Subject: [R-SIG-Finance] A question on volatility
>
> Dear all, I was trying to understand the correlation among the volatilities in different financial market, however am in dilemma what could be the rightful and acceptable-to-everyone approach. I thought to estimate the volatilities of individual markets using some GARCH modeling, then just calculate the correlation coefficient on the estimated time series of estimated daily volatilities.
>
> Is it correct approach to understand the correlation? Can somebody point me any online paper or any idea on the same?
>
> Thanks for your time.
>
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-- 
Patrick Burns
patrick at burns-stat.com
http://www.burns-stat.com
http://www.portfolioprobe.com/blog
twitter: @portfolioprobe



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