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IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation

In valuing a put-type guarantee, an actuary uses antithetic variates by pairing each stream of standard normal draws Z with -Z. Which statement best describes when this technique reduces the variance of the estimator?

Antithetic variates reduce variance when the payoff is monotonic in the random draws, because the payoffs from Z and -Z are then negatively correlated and the average of each pair has lower variance than two independent draws.

  1. AWhen the payoff is independent of the normal draws
  2. BWhen the payoff is a monotonic function of the draws, so the paired payoffs are negatively correlatedCorrect
  3. CWhen the payoff is a symmetric function of Z, so the paired payoffs are identical
  4. DWhen the number of simulations is increased to infinity only
  5. When the draws are replaced by deterministic constants

Explanation

The averaged pair has variance (sigma^2/2)(1+rho). Variance falls when rho is negative, which occurs when the payoff is monotonic in Z. A symmetric payoff gives rho=1, so no gain, which rules out option C.

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