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

In a Monte Carlo simulation of a portfolio's one-day loss, which statement about antithetic variates is correct?

Antithetic variates pair each random draw with its negative and average the two outcomes. For payoffs that move monotonically with the draw, the two results are negatively correlated, so the average has lower variance than two independent draws.

  1. AThey pair each random draw Z with its negative -Z and average the two results, which reduces variance when the payoff is monotonic in Z.Correct
  2. BThey replace random draws with a deterministic grid, so the standard error becomes exactly zero.
  3. CThey increase the number of independent trials by generating draws from a second distribution.
  4. DThey reduce bias in the estimator by correcting for discretization error in the time steps.

Explanation

Antithetic variates use Z and -Z, creating negatively correlated outputs for monotonic payoffs; averaging them lowers variance. They do not remove sampling error, do not add independent trials, and do not address discretization bias.

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