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IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation

An insurer values a maturity guarantee of Rs 10,00,000 using 10,000 simulated fund paths. At maturity, the fund value is below Rs 10,00,000 in 1,200 paths, and the average shortfall across those 1,200 paths is Rs 2,50,000. Ignoring discounting, what is the estimated cost of the guarantee per policy?

The estimated cost is Rs 30,000 per policy. The total shortfall is 1,200 times Rs 2,50,000, which is Rs 30 crore, and dividing by all 10,000 simulated paths, not just the 1,200 losing ones, gives the expected cost.

  1. ARs 30,000Correct
  2. BRs 2,50,000
  3. CRs 3,00,000
  4. DRs 20,833
  5. Rs 12,000

Explanation

The expected shortfall over all paths is the total shortfall divided by 10,000. Total shortfall = 1,200 x 2,50,000 = Rs 30,00,00,000, so the average is Rs 30,000. Rs 2,50,000 is wrong because it averages only over the paths where the guarantee bites, ignoring the 12% probability.

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