Two-State Option Pricing should not be reflected in option prices. In the appendix, we derive the Black holes equation using the two-state model. As expected, neither the growth rate nor probabilities enter the final solution. For practical applications, the two-state model appears to provide an accurate approximation to the black-Scholes model if 100 or more time differencing intervals are assumed along with any reasonable growth rate. As we show below, however, it is possible to select a growth rate that will closely approximate the value of u that minimizes the error in the two-state Finding the Best approximation According to equation(A. 11)in the Appendix, the price of a call option in the wo-state model can be stated in terms of two binomial pseudo probability distributions, In each distribution, y and are the pseudo probabilities that the price of the underlying stock will rise. These pseudo probabilities are not neces- sarily equal to the true probability, 0, but nevertheless, the mathematics of probability theory are still applicable According to the Laplace- DeMoivre Limit Theorem, it can be shown that the best fit between the binomial and normal distributions occurs when the binomial probability (or pseudo probability in this caseis -. As a general rule and will not be identical. Therefore it will usually be impossible to simultaneously set both pseudo probabilities to However, since y=p(H/(1+R)), and the term in parenthesis will generally be close to unity, the parameters of the underlying distribution that sets o to will set y to approximately By expanding o in Taylor's series, we find that o is approximately when / If the true probability, 8, is this expression simplifies to (13) For the parameters underlying Table 1, we find that(approximately) the best two-state approximation occurs when A =-.002488. The reasonableness of this result is confirmed by the u=0 panel of Table 1. We wish to acknowledge the referee for suggesting that the best approximation would occur We repeated the analysis of Table 1 by setting g to-002488. Although the prices were almost identical to those abtained by setting u to zero they were slightly more accurate