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

A Monte Carlo simulation of 400 independent trials estimates the mean payoff of an option as 6.20 with a sample standard deviation of 5.00. Using the normal approximation, which is the 95% confidence interval for the true mean payoff (use 1.96)?

The 95% confidence interval is 5.71 to 6.69. The standard error is 5.00 divided by the square root of 400, which is 0.25, and multiplying by 1.96 gives a margin of 0.49 around the sample mean of 6.20.

  1. A5.71 to 6.69Correct
  2. B5.22 to 7.18
  3. C6.10 to 6.30
  4. D3.00 to 9.40

Explanation

Standard error = 5.00/sqrt(400) = 0.25. Margin = 1.96 x 0.25 = 0.49. Interval = 6.20 ± 0.49 = 5.71 to 6.69. Using the standard deviation without dividing by sqrt(N) gives a much wider interval, and 5.22-7.18 doubles the margin.

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