In antithetic variable technique for variance reduction, the stock price path is constructed in the usual manner with positive and payoff is calculated. Then another path with negative , that is , is constructed, and payoff is calculated again. Finally, average of these two payoffs is calculated, that is
The following Matlab code calculates European-style standard call option price using antithetic variable technique for variance reduction in the Monte Carlo simulation method.
Monte Carlo using antithetic variable technique in Matlab