Efficient Monte Carlo pricing of European options¶using mean value control variates

We describe in this paper a variance reduction method based on control variates. The technique uses the fact that, if all stochastic assets but one are replaced in the payoff function by their mean, the resulting integral can most often be evaluated in closed form. We exploit this idea by applying the univariate payoff as control variate and develop a general Monte Carlo procedure, called Mean Monte Carlo (MMC). The method is then tested on a variety of multifactor options and compared to other Monte Carlo approaches or numerical techniques. The method is of easy and broad applicability and gives good results especially for low to medium dimension and in high volatility environments. Copyright Springer-Verlag Italia 2001