A Note on Modified Lattice Approaches to Option Pricing

In a recent issue of the Journal of Futures Markets, Tian (1993) investigated the numerical efficiency of various lattice models used in option valuation. Numerical efficiency was measured as the minimum number of steps required to achieve a given level of model accuracy. However, the numerical efficiency of these models was examined by using parameter values corresponding to only three different option values. Tian found with respect to call and American put options that his alternative binomial model has greater numerical efficiency than the Cox, Ross, and Rubinsteins (CRR) (1979) model. Conversely, he found with respect to European put options that the CRR model has greater efficiency than his alternative model. The purpose of this note is to document both analytically and by using a wider range of parameter values that Tian's results are not robust. No evidence is found to suggest that Tian's model is more numerically efficient than the CRR model.