During a Monte Carlo simulation you are estimating the 99% one-day Value at Risk (VaR) of a nonlinear derivatives portfolio. You have already drawn 50 000 random price paths, but the standard error of the VaR estimate is still higher than your risk-management policy allows. Which of the following changes will most effectively reduce the estimator's variance without increasing the number of simulated paths?
Increase the discretization time step so that each path contains fewer observation points.
Randomly reorder the sequence in which the simulated paths are processed during aggregation.
Generate an antithetic path (mirror image of the random shocks) for every simulated path and average the paired VaR estimates.
Re-run the simulation with a different seed to ensure a fresh set of pseudorandom numbers.
Antithetic variates create negatively correlated pairs of paths (for example, using +ε and −ε shocks). Averaging the payoffs from each pair leaves the VaR estimator unbiased while lowering its sampling variance, so the standard error falls even though the path count is unchanged. Using a coarser time grid alters discretization bias rather than sampling variance; reseeding or simply reshuffling the order of existing paths does not change the underlying distribution of draws and therefore leaves the estimator's variance essentially unaffected.
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Why does increasing the discretization time step not reduce variance?
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Why does reseeding the pseudorandom number generator not affect variance?