Antithetic paths is a kind of variance reduction techniques.
The precision of Monte Carlo Simulation is related with the simulations times. The error of results is an order of O(\(\frac{1}{\sqrt{N}}\)).
If \(X\) applies to \(\phi(0,1)\), then the antithetic variable of is \(-X\). We can call \(X\) and \(-X\) as an antithetic pair. In our implementation, when the antithetic template parameter is set to true. The RNG module will generate two random number at one clock cycles. Then, two path generators are followed to make sure it can consume two random number at on clock cycles. At the same time, the two price paths are averaged at path pricer. The structure with antithetic is as follows.
The advantage of antithetic paths is not only reducing the number of generated random number from 2N to N, but also reduces the variance of samples paths and improves the accuracy if the correlation of two antithetic variables is negative.
