Accuracy and Efficiency of Monte Carlo Method

Abstract

The accuracy of Monte Carlo method of simulating distributions is analyzed. It is shown that claimed accuracy of some standard computer codes is overstated.The correct formula for evaluation of the accuracy of any percentile (or fractile) is developed. It has been shown that increasing the accuracy of the Monte Carlo method by increasing the number of simulations is not economical because the time complexity of algorithm is inversely proportional to the squared relative error. Therefore, the new method of increasing the accuracy with a significant reduction in the number of simulations was developed. For the new method, the number of simulations and time complexity of algorithm are inversely proportional to the relative error.