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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

An insurer graduates its crude mortality rates by reference to a standard table, using the relationship q_x = a + b q_x^S, where q_x^S is the standard table rate. Which statement about this approach is correct?

The approach lets the graduated rates borrow the age pattern of the standard table while only a few parameters, here a and b, are estimated from the data. This is useful for small data sets. It does not force identical rates or guarantee that the graduation tests are passed.

  1. AIt cannot be used if the data set is small, because the standard table adds no information
  2. BIt requires the graduated rates to be identical to the standard table at every age
  3. CIt guarantees that the graduated rates will pass the chi-squared test
  4. DIt needs the standard table to be based on exactly the same population as the data
  5. It lets the graduated rates borrow the age pattern of the standard table, with only a few parameters to estimate from the dataCorrect

Explanation

Using a standard table brings in its smooth age shape, and only a and b need to be estimated. This suits small data sets. The graduated rates differ from the standard table through a and b. Passing tests is not guaranteed, and the table need not come from the same population, though it should be broadly suitable.

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