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The algorithm is certainly useful in that it is non-parametric, fast, and versatile. Meucci summarizes the advantages nicely: Unlike traditional copula techniques, CMA a) is not restricted to few parametric copulas such as elliptical or Archimedean; b) never requires the explicit computation of marginal cdf’s or quantile functions; c) does not ...

If the density of $(X,Y)$ is known, then you may obtain the density of the sum $X+Y$ simply by applying the Jacobi's transformation formula, which describes the density of the transformed random variable $g(X,Y)$ for $g(x,y) = (x+y, x)$. Integrating out the $x$-component yields the density of $X+Y$. See Jacod/Protter Probability Essentials ch. 12 for ...

In general you don't need copulas to calculate VaR on portfolio. You can use historical method if you have time series of returns for the assets in your portfolio. If you have sufficiently enough data this will allow you to take into account correlation risk, non-normality of returns. Example of code in R for equally weighted portfolio without assuming any ...

In general setting this is quite a tough problem and it looks like just switching from regular multivariate probability to copulas doesn't make it easier. In general case you need to rely on numerical methods for integration. There is a nice overview of the problem in Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25-26 ...

Look here for multivariate distribution on the positive quadrant ... quite difficult. http://xianblog.wordpress.com/tag/multivariate-analysis/ I have been thinking about this for weeks and months in the context of credit risk (modelling default intensities jointly) and I think this does not work.

It depends on the assets which copula is best and other methods may still be better and comparable in complexity. If you want to use copula's for equities you can take a look at Clayton copula. While the Gaussian copula is symmetric the Clayton copula has asymmetric tail dependency. This makes modeling the increase in correlation during a crisis possible.