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FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans

An insurer has sold 10,000 identical one-year term policies, each with a 100,000 death benefit and a true death probability of 0.5%, with deaths independent. The insurer's pricing used a mortality table assuming 0.4%. Ignoring discounting and expenses, by how much does expected claims cost exceed the amount priced in, and what does this illustrate?

Expected claims exceed the priced amount by 1,000,000, being 5,000,000 at a 0.5% death rate versus 4,000,000 at 0.4%. Because more people die than the table assumed, this is mortality risk, not longevity risk, which concerns survival exceeding expectations.

  1. A1,000,000 excess, mortality risk from underestimating mortalityCorrect
  2. B500,000 excess, longevity risk from underestimating survival
  3. C1,000,000 excess, longevity risk from underestimating survival
  4. D500,000 excess, mortality risk from underestimating mortality

Explanation

Expected claims at the true rate are 10,000 x 0.005 x 100,000 = 5,000,000. Priced claims are 10,000 x 0.004 x 100,000 = 4,000,000. The excess is 1,000,000. Deaths exceeding the table assumption is mortality risk, whereas longevity risk is people living longer than assumed.

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