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HiTo caclulate estimated correlation I use univariate garch model to estimate volatilities with for each serie of return:sigma_n=gamma+alpha* u_n-1^2+beta*sigma_n_1^2.cov_n=gamma+alpha*x_n-1 y_n-1+beta*cov_n-1Then i calculate corr(X,Y)_n=cov_n/(sigmaX_n*sigmaY_n)1°) I found that in the Hull. Do you think its a good method?2°)the product of two normal is not a normal. Estimation are done with Maximum Liklehood method. How can you do the ML estimation for cov?? What density do you use?thanks a lot

As far as I understood, the greatest problem with your approach is that you can´t garantee that the covariance matrix will not be positive definite. In the bivariate case, this would imply on a correlation > 1.I would suggest you google for multivariate Garch models. Unfortunatelly they tend to have a lot of paremeters. Unfortunatelly, tThe proper way to reduce and simplify them will have to rely on your discretion.Cheers.

I don't like it as a general approach. It assumes that correlation is a random walk, which I do not find to be a good model for the price movements of financial securities. I prefer models that assume the correlation change is either a regime shift, or the effect of a hidden variable.If you are willing to assume correlation is a random walk, that's a reasonable simple way to estimate it. Simple is good, because it's virtually impossible to distinguish among models. But be sure you test it before you use it. If it doesn't work in the past, it probably won't work in the future. If it does work in the past, it still probably won't work in the future, but you have a better shot.