Based on the Partial Distribution, we presents the concepts and expressions of DF process and DF structure and put forward the DF structure models of pricing options on a non-dividend-paying underlying for the first time. The DF structure models are able to price the call and put options exercised at any time, so it is applicable to pricing the American and European options. Finally, examples are given to compare the options priced by DF formulas and by Black-Scholes formulas, they show, as a whole, that the DF prices of options are closer to the trading prices than Black-Scholes prices in many cases.
