Correlations and Copulas

4 important questions on Correlations and Copulas

What is the deal with dependence and independence?

When we deal with normal - risk variables. Dependend variables are also correlated, independend variables are not correlated. However, when we deal with non-normal risk variables, independent variables are uncorrelated, but uncorrelated variables are not necessary independent.

What are the three rules of copulas?

Copulas are monotonicit (they are a joint CDF), they have uniform marginals and non-negative probabilities

What is a copula?

A copula is a special type of distribution function which is used to describe (or build) the dependence between two or more random variables. It describes the dependence structure among the components.

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The joint distribution of a random vector can be written in terms of marginal distribution functions and a copula. What do the marginals describe?

The marginals describe the marginal distribution of each component of the random vector, while the copula describes the dependence structure among the components.

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