medium · Quantitative Finance numerical
When using a control variate X to estimate Y, what happens if the two variables are perfectly uncorrelated?
- The estimator becomes biased and fails to converge to the true mean.
- The standard error of the estimate increases by a factor of roughly √(2).
- The variance of the estimate is reduced all the way down to exactly zero with certainty.
- The variance of the estimate remains the same as the raw Monte Carlo variance.
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