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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

A risk analyst uses Monte Carlo simulation to estimate the expected payoff of a derivative. With 10,000 independent simulated payoffs, the standard error of the estimated mean is 0.40. The analyst wants to cut the standard error to 0.10 by increasing the number of simulations only. How many simulations are required?

160,000 simulations are needed. Standard error falls with the square root of N, so reducing it fourfold from 0.40 to 0.10 requires sixteen times as many draws: 10,000 x 16 = 160,000. Quadrupling N to 40,000 would only halve the error.

  1. A40,000
  2. B80,000
  3. C160,000Correct
  4. D1,000,000

Explanation

Standard error is sigma divided by the square root of N. Cutting it by a factor of 4 (0.40 to 0.10) requires N to rise by 4^2 = 16. So N = 10,000 x 16 = 160,000. Choosing 40,000 wrongly scales N by the same factor as the error reduction.

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