Dynamic copula with Garch

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amadei
Posts: 1
Joined: Thu Aug 12, 2010 4:22 pm

Dynamic copula with Garch

Postby amadei » Thu Aug 12, 2010 9:34 pm

Dear Professor,
Do you have any recommendations for how to incorporate both time varying multi variate dependence via copula with Garch for individual securities/factors to simulate returns so that returns are not just dependent but also path dependent? In your vol.4, you covered static copula examples with iid assumptions or cases where it's the correlation/covariance that was time varying. I'm particularly interested in your suggestions regarding Clayton-Garch method, if available to move away from correlation based methods so that asymmetric, time varying dependence is incorporated along with volatility clustering. In the book for Example 4.14, you use multi variante GARCH to incorporate time varying dependence but is not recommended by you for more than a few securities/assets and moreover, the assumption of elliptical distribution where correlation is relevant is also limiting.

Would the following method be appropriate - for example, 1) use a rolling window (200 days) to calibrate copula and to produce simulated dependent variables (e.g., for t distribution); 2) use these variables to produce simulated forecasts of volatilities and returns; 2) repeat? My concern is that such an approach won't capture changes in the environment quickly. Perhaps, that can be moderated by using copulas calibrated on different environments - e.g., normal vs crash- just as one can use normal and stress covariance matrix

Any recommendations are much appreciated.

Thank you very much for your time and great writing!

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Dynamic copula with Garch

Postby coalexander » Fri Aug 13, 2010 9:17 am

Hi

In a multivariate copula set-up the copula captures the dependence (like a generalization of correlation - indeed, when you use correlation people call this the Gaussian copula) and the marginals (ie the individual univariate distributions) are mopdelled separately.

You can still model the variances of the marginal distributions as GARCH models and then employ a static copula framework, and in many applications this would be advisable. Indeed it is akin to Bollerslev's Constant Correlation Garch model. I would start with this framework, and then consider adding a simple (EWMA?) model to the copula parameters, to allow them to evolve over time, to see how much information this can add. Only if it seems that copula parameters are time-varying in an INTUITIVE way (ie look at their sample paths and see whether you can interpret why they go up and down in terms of events in the markets) should you consider tackling the full thing.

Trying to add time-variation to the copual parameters is difficult, and I have not done this myself. `:roll:` However, I have a friend who has! `:D` I attach a paper on this subject, and you can also find matlab code on Andrew Patton's website: http://econ.duke.edu/~ap172/code.html [see No. 7 "New" `:!:` copula toolbox]

Cheers, Carol


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