medium · Quantitative Finance numerical
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 two regardless of the correlation coefficient rho between paths.
- It increases because M/2 pairs is inherently a much smaller effective sample size than the original M.
- It remains exactly s/sqrt(M) because the total number of simulated paths generated is still M in aggregate.
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