# A question on volatility

7 messages
Open this post in threaded view
|

## 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. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
Open this post in threaded view
|

## Re: A question on volatility

 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: [hidden email] [mailto:[hidden email]] On Behalf Of Megh Dal Sent: Wednesday, October 05, 2011 12:15 PM To: [hidden email] 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. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
Open this post in threaded view
|

## Re: A question on volatility

 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: [hidden email] [mailto:[hidden email]] On Behalf Of Megh Dal > Sent: Wednesday, October 05, 2011 12:15 PM > To: [hidden email] > 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. > > _______________________________________________ > [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. > > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. > -- Patrick Burns [hidden email] http://www.burns-stat.comhttp://www.portfolioprobe.com/blogtwitter: @portfolioprobe _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
Open this post in threaded view
|

## Re: A question on volatility

 I agree with Pat. Time varying correlations in a multivariate GARCH model are different from the correlations between volatility series. Because volatility is "unobservable" (i.e, except for special cases like the VIX) and derived measures like implied volatility are model based (e.g. derived from Black-Scholes) it is not straightforward to define and measure correlations between volatilities. One model-based approach in which volatility is a random variable is the stochastic volatility model. One can build multivariate models in which the correlation to volatility shocks is parameterized (but this is not the correlation between volatilities). GARCH models produce very noisy estimate of volatility and so the correlations computed from GARCH volatilities are likely to be very  noisy as well. A better approach would be to compute volatilities using intra-day high frequency data (e.g. realized volatility) - see the realized package. This would give you much more precise estimates of volatility. Then the problem would be to model the correlation between the observed volatilities. For example, simple EWMAs. One could even consider a simple vector autoregressive model for a multi-variate time series of volatilities. This is what Andersen, Bollerslev, Diebold and Labys did in their Econometrica paper. One potential problem is that the realized volatility series tend to be non-stationary. Just some thoughts. -----Original Message----- From: [hidden email] [mailto:[hidden email]] On Behalf Of Patrick Burns Sent: Wednesday, October 05, 2011 1:39 PM To: [hidden email] Subject: Re: [R-SIG-Finance] A question on volatility 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: [hidden email] [mailto:[hidden email]] On Behalf Of Megh Dal > Sent: Wednesday, October 05, 2011 12:15 PM > To: [hidden email] > 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. > > _______________________________________________ > [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. > > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. > -- Patrick Burns [hidden email] http://www.burns-stat.comhttp://www.portfolioprobe.com/blogtwitter: @portfolioprobe _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
Open this post in threaded view
|