medium · Quantitative Finance
In a Monte Carlo simulation, if the sample standard deviation of the payoff is s and the number of paths is M, the standard error is s/√(M).
If we use M/2 antithetic pairs instead, what happens to the standard error?
- It becomes s_pair/√(M/2), where s_pair is the standard deviation of the pair average
- It is reduced by a factor of 2 regardless of the correlation ρ
- It increases because M/2 is a smaller sample size than M
- It remains exactly s/√(M) because the total number of paths is still M
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