Abstract: To overcome the volatility of the binomial tree option price model's convergence, and to strengthen the predictive effect of the historical data information, we propose a novel tree model that is smooth and convergent. Based on the historical data information, the new model applies the minimum cross entropy formalism to derive the crucial parameters p,u and $d$ of the binomial tree option price model, and the backward induction is used to compute the option
price. Obviously, option price computed by the new model implies the historical data information. Because the minimum cross entropy formalism is a convex optimization problem, it has the unique optimal solution. Furthermore, the new model is also suitable for pricing the option in the incomplete market. Finally, compared with the CRR model, the new one can smoothly converge and have more accurate results in numerical examples. Moreover, the new model can
converge to the B-S formula for the call (put) European option (binary option).    

Key words: binomial tree option pricing model, smooth convergence ,  minimum cross entropy formalism, prior probability