Antithetic Variates

Antithetic variates is a variance reduction technique that uses pairs of negatively correlated random variables to improve the precision of a simulation. In the context of options pricing, for every path generated using a set of random shocks, a second path is generated using the exact negative of those shocks.

By averaging the results of these two paths, the variance of the overall estimate is reduced because the fluctuations in the first path are partially offset by the second. This method is computationally inexpensive and easy to implement, making it a popular choice for improving the efficiency of Monte Carlo simulations in derivatives pricing.

It effectively cancels out some of the randomness, leading to faster convergence to the true price. In crypto derivative platforms, this can be used to speed up the calculation of Greeks for large portfolios of options.

It represents a simple yet powerful way to extract more information from each simulation trial. By ensuring that the random inputs are balanced, the simulation provides a more stable and reliable output for traders.