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

An insurer runs a nested (stochastic-on-stochastic) simulation to find the 99.5th percentile of the one-year loss on a guarantee book. There are 1,000 outer real-world scenarios, and in each the year-end liability is valued with 500 inner risk-neutral paths. Which statement about this design is correct?

The design uses 500,000 paths in total, and sampling noise in each inner liability estimate adds spread to the outer loss distribution. This tends to overstate extreme percentiles such as the 99.5th, so inner error cannot be ignored.

  1. AInner simulation error disappears because outer scenarios are real-world
  2. BTotal path count is 500,000 and inner noise adds variance to the estimated liabilities, tending to overstate the tail of the loss distributionCorrect
  3. CTotal path count is 1,500 and inner noise has no effect on percentiles
  4. DUsing risk-neutral inner paths means the outer scenarios must also be risk-neutral
  5. Increasing inner paths raises the sampling error of the outer percentile

Explanation

Paths total 1,000 x 500 = 500,000. Each inner liability estimate has sampling error, which adds noise to the outer distribution and so widens it, biasing extreme percentiles upward. Option A is wrong since inner error remains. Option E is wrong since more inner paths reduce inner noise.

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