[R-SIG-Finance] A question on volatility

[Eric Zivot]

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: r-sig-finance-bounces at r-project.org
[mailto:r-sig-finance-bounces at r-project.org] On Behalf Of Patrick Burns
Sent: Wednesday, October 05, 2011 1:39 PM
To: r-sig-finance at r-project.org
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/OrthogonalG
ARCH_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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