This paper has two researches direction, one is in the pricing and application of a probation option, the other is in the pricing and application of an American option. In the research of a probation option, this paper used the concept of the marketing strategy to be the source of financial innovation, and therefore decision a new exotic option. We call this option is a probation option. We introduce the application of this option, and further more to device the value of this option. Beside, this option also can apply to the field of marketing, and to calculate the cost of marketing strategy. In the research of an American, this paper proposes a new method- the implied belief model, to obtain a closed-form solution of the value of the American option. We analyze the value of the American option through the view point of the sellers of the options. By adopting this method, we derive the upper bound for the value of an American option. Then we define the belief value of seller to obtain a closed-form solution of the value of an American option. Finally, we apply the method to S&P 100 American option and deduce the implied belief value.