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

Which statement about variance reduction techniques in Monte Carlo simulation is most accurate?

Antithetic variates reduce variance when the payoff is monotonic in the underlying random draw, because the outcomes from a draw and its mirror image are then negatively correlated and partly offset each other when averaged.

  1. AAntithetic variates reduce variance only when the payoff is a monotonic function of the random draw, since this makes the paired outcomes negatively correlatedCorrect
  2. BControl variates work best when the control has a correlation with the target close to zero
  3. CVariance reduction techniques remove sampling error entirely, so the standard error becomes zero
  4. DAntithetic variates double the number of independent draws, halving the standard error

Explanation

For a monotonic payoff, the outcomes from Z and -Z are negatively correlated, so averaging them lowers variance. Control variates need high absolute correlation, not near zero. Variance reduction lowers but does not eliminate sampling error, and antithetic pairs are not independent draws.

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