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

A risk manager at an Indian general insurer aggregates losses from fire and marine cargo lines and is worried that severe losses tend to occur together in catastrophe years. Which copula choice is most appropriate to capture this feature, and why?

The Gumbel copula is most suitable because it exhibits upper tail dependence, meaning extreme large losses are more likely to occur together. Clayton has lower tail dependence, while Gaussian, Frank and independence copulas show no tail dependence, so they would understate joint catastrophe losses.

  1. AA Gumbel copula, because it has upper tail dependenceCorrect
  2. BA Clayton copula, because it has upper tail dependence
  3. CA Gaussian copula, because it has strong tail dependence
  4. DA Frank copula, because it has strong upper tail dependence
  5. The independence copula, because it has symmetric tail dependence

Explanation

Joint large losses require upper tail dependence. The Gumbel copula has upper tail dependence and no lower tail dependence. Clayton has lower tail dependence, while Gaussian and Frank have none in the tails, and independence has none.

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