IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas
The Clayton copula has generator φ(t) = (t^(-θ) - 1)/θ with θ > 0, giving C(u,v) = (u^(-θ) + v^(-θ) - 1)^(-1/θ). For θ = 1, u = 0.5 and v = 0.5, what is C(u,v)?
C(0.5,0.5) equals 0.3333. Substituting θ = 1 gives (2 + 2 - 1)^(-1) = 1/3. This exceeds the independence value of 0.25, reflecting positive dependence in the Clayton copula.
- A0.2500
- B0.3333Correct
- C0.5000
- D0.2000
- 0.4000
Explanation
With θ = 1: u^(-1) = 2 and v^(-1) = 2. Sum minus 1 = 2 + 2 - 1 = 3. Raising to the power -1 gives 1/3 = 0.3333. The value 0.25 would be the independence copula, which ignores the dependence.
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