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

A Clayton copula with parameter a = 2 is used for two risks. Using the lower tail dependence coefficient of the Clayton copula, 2^(-1/a), what is the probability, in the limit, that one risk is in its lowest tail given that the other is, and how does this compare with the same copula with a = 1?

The coefficient is 0.7071 for a = 2 and 0.5 for a = 1. Since 2^(-1/a) rises as a increases, a larger Clayton parameter means stronger lower tail dependence between the two risks.

  1. A0.5 for a = 2, against 0.7071 for a = 1
  2. B0.7071 for a = 2, against 0.5 for a = 1Correct
  3. C0.25 for a = 2, against 0.5 for a = 1
  4. D0.7071 for a = 2, against 0.25 for a = 1
  5. 0.5 for a = 2, against 0.25 for a = 1

Explanation

For a = 2, 2^(-1/2) = 0.7071. For a = 1, 2^(-1) = 0.5. Larger a gives stronger lower tail dependence. Option one reverses these values, which is the mistake of treating dependence as decreasing in a.

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