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

Which statement about tail dependence in common copulas is correct?

The Clayton copula with a positive parameter has lower tail dependence and no upper tail dependence. Gumbel is the reverse, while Gaussian, Frank and independence copulas are tail independent, which makes Clayton suitable for modelling joint extreme lows.

  1. AThe Gaussian copula with correlation below 1 has positive upper tail dependence
  2. BThe Clayton copula with positive parameter has lower tail dependence but no upper tail dependenceCorrect
  3. CThe Gumbel copula has lower tail dependence but no upper tail dependence
  4. DThe independence copula has tail dependence coefficient 0.5
  5. The Frank copula has positive tail dependence in both tails

Explanation

The Clayton copula with positive parameter has lower tail dependence of 2^(-1/alpha) and zero upper tail dependence. The Gaussian copula with correlation below 1 is tail independent. The Gumbel copula has upper, not lower, tail dependence. The independence and Frank copulas have no tail dependence.

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