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

An actuary compares a Gaussian copula and a t copula, both with the same correlation matrix, for modelling joint extreme claims from two lines of business. Which statement is correct about the t copula?

The t copula has symmetric upper and lower tail dependence, and this dependence weakens as the degrees of freedom increase. In the limit it approaches the Gaussian copula, which has no tail dependence, so it captures joint extremes better at low degrees of freedom.

  1. AIt has zero tail dependence, like the Gaussian copula, for all degrees of freedom
  2. BIt has symmetric upper and lower tail dependence, which falls as the degrees of freedom increaseCorrect
  3. CIt has upper tail dependence only
  4. DIt has lower tail dependence only, which rises as the degrees of freedom increase
  5. It converges to the independence copula as the degrees of freedom tend to infinity

Explanation

The t copula has equal positive upper and lower tail dependence for correlation above -1 and finite degrees of freedom. As the degrees of freedom rise, tail dependence decreases and the copula tends to the Gaussian copula, not to independence unless the correlation is zero.

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