Pricing the American put option: A detailed convergence analysis for binomial models

Abstract

Leisen and Reimer (1996) suggested to consider the order of convergence as a measure of convergence speed for European call options. In this paper we study in a first step the problem of determining the order of convergence in pricing American put options for several approaches in the literature. We will then examine in detail extrapolation and the Control Variate technique for improving convergence and will explain their pitfalls. Since the investigation reveals the need for smooth converging models in order to get smaller initial errors, such a model is constructed. The different approaches are then tested: simulations exhibit up to 100 times smaller initial errors.