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

A simulation of an option payoff X has variance 16. The analyst uses a control variate Y with variance 4 and correlation 0.8 with X, where E[Y] is known. Using the optimal coefficient, what is the variance of the adjusted estimator for a single draw?

The adjusted variance is 5.76. With the optimal coefficient, a control variate reduces variance to Var(X)(1-ρ²), which is 16 × (1-0.64) = 5.76. The control variate's own variance does not enter the final result.

  1. A5.76Correct
  2. B6.40
  3. C10.24
  4. D16.00

Explanation

With the optimal coefficient, the variance of the adjusted estimator is Var(X)(1-ρ²) = 16 × (1-0.64) = 16 × 0.36 = 5.76. The 10.24 figure is 16 × (1-0.36), which wrongly uses ρ² = 0.36 as if it were the correlation squared of 0.6. The 6.40 figure uses 16 × (1-0.6), which treats ρ as 0.6.

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