Abstract

In this talk we will discuss two issues for the accuracy of the Monte-Carlo methods for valuing American options: the discretization error and the variance reduction techniques. At the present stage, the variance reduction technique is the main issue which is discussed in the literature and the explicit Euler method is dominant in application. By applying numerical methods with different order, we indicate that the accuracy of the numerical methods is very important in the Monte-Carlo simulation method. It is strongly recommended to use numerical methods with higher order and with better stability properties. For the one-factor and two-factor model for commodity prices, we discuss the efficiency of the variance reduction techniques which is based on the high order numerical methods and Monte-Carlo method for valuing American options.

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