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

A life insurer values a guarantee at a future time horizon using nested (stochastic-on-stochastic) simulation: 1,000 outer real-world scenarios, each with 500 inner risk-neutral paths to value the guarantee at the horizon. Which statement is correct?

Nested simulation needs 1,000 times 500, or 500,000, paths, and the sampling noise in the inner valuations spreads out the outer distribution, which can overstate tail measures. Inner paths are risk-neutral, and more outer scenarios do not remove inner error.

  1. ATotal path count is 1,500 because outer and inner paths are added
  2. BThe inner valuations are unbiased for the nonlinear tail measure such as a 99.5th percentile, whatever the inner count
  3. CInner paths must use real-world drift, matching the outer scenarios, to value the guarantee
  4. DTotal path count is 500,000, and inner-sampling error makes the outer distribution more dispersed than the true one, which can overstate tail capitalCorrect
  5. Increasing outer scenarios alone removes the inner-simulation error

Explanation

Nested simulation multiplies paths: 1,000 x 500 = 500,000. Inner estimates carry noise, which adds variance to the outer distribution of values, so extreme percentiles can be overstated. Inner valuation uses risk-neutral measure for market-consistent value, and more outer scenarios do not cure inner error.

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