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I have seen plenty of literature about GARCH on estimation volatility. how about covariance? There are plenty of risk models depending on the covariance matrix.

I guess we can assume the correlation is constant and volatility changes. But in reality in super volatile moment correlation between stocks increases.

Or there is a separate model for estimating correlation?

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I think you're looking for multivariate GARCH models of which this is an overview paper.

Multivariate GARCH models have one big drawback: they are pretty hard to estimate due to the number of correlations. This paper by Caporin and McAleer might be of interest in that regard.

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Not sure your question is about having a process for covariance or to have multivariate GARCH.

The standard viewpoint on a stochastic volatility for covariance is to use a Whishart process. See for instance Philipov, A. and M. E. Glickman (2006, July) Multivariate stochastic volatility via wishart processes. Journal of Business & Economic Statistics 24 (3), 313-328. You will find all the formulas.

Just note in dimension one, it is like using a Gamma distribution for your volatility, using a "time serie" (a stochastic process) on the parameter $\beta$. I.e.

$$X_t|\sigma^2_t \sim {\cal N}(0, \sigma_t)$$

and

$$\sigma_t^{-2}|\alpha,\beta_t\sim \Gamma(\alpha,\beta_t).$$

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