Efficient multiple control variate method with applications to exotic option pricing

摘要

The Monte Carlo simulation method is still the only feasible approach to handle high dimensional problems encountered in many areas so far. The main drawback of this method is its slow convergence. A variance reduction technique is one of the main methods to speed up Monte Carlo simulations. In this paper, we reconsider the multiple control variate method and provide sufficient conditions to ensure that the variance of an m-variate control variate estimator is smaller than that of a k-variate control variate estimator for any k where . The results can be applied to a wide range of high dimensional complex problems where exact solutions do not exist. As nontrivial examples, the results are applied to problems of options pricing under the Black-Scholes-Merton's model. For arithmetic Asian and basket options, more efficient new control variate estimators are constructed. Numerical results show that the constructed multiple control variate estimators are more efficient than estimators with fewer control variates in reducing variances.