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

A Gaussian copula with correlation parameter 0.6 is used to link two loss variables. Which statement about its tail dependence is correct?

The Gaussian copula with correlation 0.6 has no tail dependence in either tail. Tail dependence coefficients are zero for any correlation below 1, so extreme losses become asymptotically independent despite the positive correlation in the body of the distribution.

  1. AIt has positive upper and lower tail dependence because the correlation is positive
  2. BIt has upper tail dependence only
  3. CIt has lower tail dependence only
  4. DIt has no tail dependence in either tail for any correlation below 1Correct
  5. It has tail dependence that increases as the sample size increases

Explanation

For the bivariate Gaussian copula, the coefficients of upper and lower tail dependence are both zero whenever the correlation is strictly less than 1. A positive correlation of 0.6 gives dependence in the centre of the distribution but not asymptotically in the tails. The first option confuses positive correlation with tail dependence.

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