IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation
An actuary values a maturity guarantee on a unit-linked contract using 10,000 independent stochastic simulations of the fund value. She wants the standard error of the estimated mean guarantee cost to be halved, keeping the same method. Approximately how many simulations are needed?
About 40,000 simulations are needed. The standard error of a Monte Carlo estimate falls with the square root of the number of runs, so halving the error requires four times as many simulations, not twice as many.
- A20,000
- B40,000Correct
- C15,000
- D80,000
- 100,000
Explanation
Standard error of a Monte Carlo mean is sigma divided by the square root of n. Halving it needs the square root of n to double, so n must be multiplied by 4, giving 40,000. Doubling to 20,000 only reduces the error by a factor of about 1.41.
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