Portfolio Value-at-Risk estimated using the copula approach often just means generating artificial data sampled from a parametric copula('s joint multivariate distribution) as a model fit over the real data, and then estimating VaR from this artificial data,
but is there any actual equivalence or connection between the copula and Value-at-Risk measure? In other words, is VaR actually equivalent or mathematically linked to copula somehow, using integrals and probabilities?
From what I know, VaR just measures the quantiles in the tails of joint distributions, whereas copula is an estimate or fit of the entire joint distribution, not just tails. Why would anyone have thought this would be a good idea in the first place knowing that these concepts operate over two distinct regions?