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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection

The Cairns-Blake-Dowd (CBD) model for older ages is logit q(x,t) = k1(t) + k2(t)(x - xbar). Which statement about it is correct?

In the CBD model, k1(t) is the time-varying level of logit mortality across ages and k2(t) is the time-varying slope against age relative to the mean age xbar. Both are period effects, and a cohort term appears only in extended versions.

  1. Ak1(t) is an age-specific constant and k2(t) a cohort effect
  2. Bk1(t) gives the overall level of logit mortality across ages and k2(t) gives the slope with respect to age, both varying with timeCorrect
  3. Ck1(t) and k2(t) are fixed parameters that do not change over time
  4. DThe model uses a separate parameter for every age, so it has many more parameters than Lee-Carter
  5. The model includes a cohort term as standard, with k2(t) acting as the cohort index

Explanation

In the basic CBD model both k1(t) and k2(t) are period effects. k1 is the level of logit q across ages and k2 is the slope against (x - xbar). Cohort terms appear only in extensions, and the model has no age-specific parameters.

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