Abstract
In this paper we re-examine the American-style option pricing formula of Geske and Johnson (1984) and extend the analysis by deriving a modified formula that can overcome the possibility of non-uniform convergence encountered in the original Geske-Johnson methodology. Furthermore, we propose a numerical method, the Repeated-Richardson extrapolation, which allows us to estimate the interval of true option values and to determine the number of options needed for an approximation to achieve a given desired accuracy. Using simulation results, our modified Geske-Johnson formula is shown to be more accurate than the original Geske-Johnson formula. This paper also illustrates that the Repeated-Richardson extrapolation approach can estimate the interval of true American option values extremely well. Finally, we investigate the possibility of combining the Binomial Black-Scholes method proposed by Broadie and Detemple (1996) with the Repeated-Richardson extrapolation technique.
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