Antithetic variates

In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error reduction in the simulated signal (using Monte Carlo methods) has a square root convergence, a very large number of sample paths is required to obtain an accurate result. The antithetic variates method reduces the variance of the simulation results.

The antithetic variates technique consists, for every sample path obtained, in taking its antithetic path — that is given a path ${\displaystyle \{\varepsilon _{1},\dots ,\varepsilon _{M}\}}$ to also take ${\displaystyle \{-\varepsilon _{1},\dots ,-\varepsilon _{M}\}}$. The advantage of this technique is twofold: it reduces the number of normal samples to be taken to generate N paths, and it reduces the variance of the sample paths, improving the accuracy.

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