Most natural generalization of covariance/correlation to model dependence of extreme events [closed]

Question

One of the most serious shortcomings of covariance/correlation are the assumptions of linearity and normality.

What is the most natural generalization of these measures of dependence when you want to model the dependence structure of extreme events using heavy-tailed distributions, e.g. the Generalized extreme value distribution?

With "most natural generalization" I mean that the classical covariance/correlation is included as a special case when the usual assumptions hold.

(Disclosure: After having received no answers for nearly two weeks I posted this question also at Quantitative Finance)

Answer 1

I guess the answer really depends on what you want to do with it! It is tricky to measure association for extreme values, not the least because the correlation structure often will change in the extreme tails. Look at the stock exchange. Papers that in normal times do not correlate much, will tend to correlate more in time of crisis, since then all the papers move downwards.

Things you could look into: tail dependence coefficients, write into google "tail dependence coefficients" (without the "")

Extreme value copulas: Write into google "copula of extreme value distributions" (without the "")