Control variates

Quantitative Finance Glossary

Variance-reduction technique using a correlated random variable Y with known mean mathbbE[Y]: estimator hatθ_CV = barX - β,(barY - mathbbE[Y]), optimal β^* = Cov(X,Y)/Var(Y), yielding variance Var(hatθ_CV) = (1 - ρ_XY^2),Var(barX). Pricing an arithmetic Asian by Monte Carlo using the geometric Asian (closed form under GBM) as a control is the canonical example — variance can drop 100×.

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