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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas

Which statement about tail dependence coefficients is correct?

Tail dependence coefficients are unchanged by strictly increasing transformations of the variables, because they depend only on the copula and not on the marginals. They need not be equal in both tails, and a value of 1 means strong, not zero, dependence.

  1. AThey depend on the marginal distributions as well as the copula
  2. BThey are unchanged by strictly increasing transformations of each variableCorrect
  3. CA coefficient of 1 means the variables are independent
  4. DThey equal Pearson's correlation in the tails
  5. The lower and upper coefficients must always be equal

Explanation

Tail dependence depends only on the copula, and a copula is invariant under strictly increasing transformations of the marginals. So the coefficients do not change under such transformations. A coefficient of 1 indicates perfect dependence in the tail, not independence. Lower and upper values can differ, as for Clayton.

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