IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas
A Clayton copula has C(u,v) = (u^(-a) + v^(-a) - 1)^(-1/a) with a = 2. Using the lower tail dependence formula for this copula, what is the lower tail dependence coefficient?
The lower tail dependence coefficient is 2^(-1/2), which is about 0.7071. For a Clayton copula the coefficient is 2 raised to the power minus one over the parameter, so a parameter of 2 gives this value.
- A0.25
- B0.50
- C0.7071Correct
- D0.8409
- 1.00
Explanation
Lower tail dependence for Clayton is 2^(-1/a). With a = 2 this is 2^(-0.5) = 0.7071. Choosing 0.25 uses 2^(-a), the wrong exponent. The value 0.50 would come from a = 1.
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