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

A Monte Carlo analyst compares a simulation using antithetic variates with one using the same number of independent draws. Which statement best describes why antithetic variates can reduce the standard error of the estimate?

Antithetic variates pair each draw z with -z, producing negatively correlated payoffs for monotonic payoff functions. The average of each pair then has lower variance than two independent draws, reducing the standard error of the Monte Carlo estimate.

  1. AEach pair of draws uses z and -z, giving negatively correlated payoffs whose average has lower variance when the payoff is monotonic in zCorrect
  2. BEach pair uses the same z twice, so the number of random numbers generated is halved without changing variance
  3. CThe method replaces random draws with a deterministic grid, eliminating sampling error entirely
  4. DThe method increases the sample standard deviation so that confidence intervals are wider and more conservative

Explanation

Antithetic variates pair z with -z. For a payoff monotonic in z, the two payoffs are negatively correlated, so the variance of their average is less than that of two independent draws. Reusing the same z gives perfect positive correlation and does not help; the method does not remove sampling error.

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