Accuracy issues of Monte-Carlo methods for valuing American options

Abstract

In this paper we discuss accuracy issues of the Monte-Carlo method for valuing American options. Two major error sources are discussed: the discretization error of numerical methods for simulating stochastic models and the statistical error of finite samples. As the explicit Euler method is dominant in the extant literature of computational finance, it is strongly recommended to use numerical methods with higher convergence order to reduce the discretization error. In this paper we use the trapezoidal method for simulating the one-factor and two-factor models for commodity prices. For the Monte-Carlo method for valuing American options, variance reduction techniques are applied to reduce the statistical error.