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

A risk modeller is choosing between a bivariate Gaussian copula and a bivariate Student's t copula with the same correlation parameter and 4 degrees of freedom to model joint losses from two portfolios. Which statement is correct?

The t copula with finite degrees of freedom has positive tail dependence in both tails, even at zero correlation. The Gaussian copula has no tail dependence unless the correlation is perfect, so it understates joint extreme events relative to the t copula.

  1. AThe Gaussian copula has positive lower and upper tail dependence whenever the correlation is positive
  2. BThe t copula has positive tail dependence in both tails even when the correlation is zero and the degrees of freedom are finiteCorrect
  3. CThe t copula has zero tail dependence when the degrees of freedom are finite
  4. DThe t copula has positive tail dependence only in the upper tail
  5. Both copulas have identical tail dependence because they share the same correlation

Explanation

The t copula with finite degrees of freedom has symmetric positive lower and upper tail dependence for any correlation parameter above -1, including zero. The Gaussian copula has zero tail dependence for correlation below 1, so the first option is wrong.

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