Richardson Extrapolation Techniques for Pricing American-style Options

In this paper we re-examine the Geske-Johnson formula (1984) and extend the analysis by deriving a modified Geske-Johnson formula that can overcome the possibility of non-uniform convergence encountered in the original Geske-Johnson formula. Furthermore, we propose a numerical method, the repeated Richardson extrapolation, which is able to estimate the interval of true option values when the accelerated binomial option pricing models are used to value American-style options. We also investigate the possibility of combining the Binomial Black and Scholes method proposed by Broadie and Detemple (1996) with the repeated Richardson extrapolation technique. From the simulation results, our modified Breen accelerated binomial model is as fast, but on average more accurate than, the Breen accelerated binomial model. We lastly illustrate that the repeated Richardson extrapolation approach can estimate the interval of true American option values extremely well.