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

A risk manager at an Indian general insurer models flood and cyclone losses and finds they tend to be extreme together far more often than a bivariate normal with the same correlation would suggest. Which feature, and the copula that best captures it, is correct?

Joint extreme losses indicate upper tail dependence, which the Gumbel copula captures. The Gaussian and Frank copulas have no tail dependence and would understate simultaneous large losses, while the Clayton copula has lower rather than upper tail dependence.

  1. ALower tail dependence; the Clayton copula
  2. BUpper tail dependence; the Gumbel copulaCorrect
  3. CUpper tail dependence; the Gaussian copula
  4. DZero tail dependence; the Frank copula
  5. Zero tail dependence; the independence copula

Explanation

Large losses occurring together is upper tail dependence. The Gumbel copula has upper tail dependence, whereas the Clayton has lower tail dependence. The Gaussian and Frank copulas have no tail dependence (for correlation below 1), so they would understate joint extremes.

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