Pricing the American Put Option: A Detailed Convergence Analysis for Binomial Models
Posted: 3 Jul 1998
Date Written: February 1996
Viewing binomial models as a discrete representation of the respective continuous models, the interest focuses on the notions of convergence and especially "fast" convergence. Though the problem of better performance was addressed by many authors, none of these could successfully explain this for their proposed models, since they all lacked a measure of convergence speed. In the case of the European call option Leisen and Reimer examined convergence speed by the order of convergence in a rigorous framework. However the analysis could not be transformed to the case of American put options. One aim of this paper is thus to generalize the ideas to the more interesting case of the American put option. It follows that the models of Cox, Ross and Rubinstein, Jarrow and Rudd and Tian are all equal in this sense. Moreover this amounts to an intuitive proof of convergence of prices that is independent from those of Kushner and Lamberton and Pages. In a second step an error representation is derived using the concept of order of convergence. This allows for determination of the correct extrapolation rule and its error analysis. Since the investigation reveals the need for smooth converging models in order to get smaller initial errors, such models are constructed. The different approaches are then tested: simulations exhibit up to 100 times smaller initial errors.
JEL Classification: G13
Suggested Citation: Suggested Citation