Skip to content

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

A risk manager runs a Monte Carlo experiment with N = 10,000 and obtains a standard error of 0.50 for an option price estimate. She applies antithetic variates, which reduces the standard deviation of the estimator by 40% at the same N. With the reduced variance, what number of simulations of the original (plain) method would give the same standard error as the improved estimator at N = 10,000?

About 27,778 plain simulations. Antithetic variates cut the standard error from 0.50 to 0.30. Since error scales with one over the square root of N, the plain method needs (0.50/0.30) squared, about 2.778 times as many trials, so 10,000 x 2.778 is roughly 27,778.

  1. A16,000
  2. B27,778Correct
  3. C36,000
  4. D25,000

Explanation

New standard error = 0.50 x 0.60 = 0.30. Plain method needs 0.50 x sqrt(10,000/N) = 0.30, so sqrt(N/10,000) = 0.50/0.30 = 1.6667, N = 10,000 x 2.7778 = 27,778.

Did you get it right without looking?

One question tells you little. A timed set on Simulation and Bootstrapping shows your real accuracy, how long you take and where you lose marks.

Practise Simulation and BootstrappingFree diagnostic mock

More Simulation and Bootstrapping questions