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

In simulating the cost of a put-style maturity guarantee, antithetic variates are used by pairing each path generated from standard normal draws Z with a path generated from -Z. Under which condition does this reduce the variance of the estimator?

Antithetic variates reduce variance when the paired payoffs are negatively correlated, which is assured when the payoff is a monotonic function of the normal draws. Positive correlation or a symmetric payoff gives no improvement.

  1. AThe payoff is a monotonic function of the underlying normal draws, so the paired payoffs are negatively correlatedCorrect
  2. BThe payoff is independent of the normal draws
  3. CThe number of simulations is doubled while the seed is changed
  4. DThe payoff is a symmetric function of Z about zero
  5. The paired payoffs are positively correlated

Explanation

The average of a pair has variance (sigma squared/2)(1+rho). Variance falls when rho is negative, which is guaranteed when the payoff is monotonic in Z. A symmetric payoff would give identical paired values, rho=1, and no gain.

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