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

Two loss variables X and Y are linked by a Clayton copula with parameter α = 2, where C(u,v) = (u^(-α) + v^(-α) − 1)^(-1/α). The lower tail dependence coefficient is 2^(-1/α). What is its value, to three decimal places?

The lower tail dependence coefficient is 2^(-1/2) = 0.707. Substituting α = 2 into the Clayton formula gives the reciprocal of the square root of 2, showing substantial dependence between joint extreme low outcomes.

  1. A0.250
  2. B0.500
  3. C0.707Correct
  4. D0.354
  5. 0.841

Explanation

Lower tail dependence = 2^(-1/2) = 1/√2 = 0.707. A value of 0.354 comes from mistakenly dividing by another factor of 2, and 0.5 or 0.25 come from using 2^(-1) or 2^(-2).

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