Abstract
The crucial problem of researching Option Theory is calculate the reasonable value of Options. For Option Pricing Model, We can divide it into two cases, which are Discrete-time model and Continuous-time model. This paper analysis the two models for some examples, which include paying dividend and not paying dividend. this paper analysis Stock ,Cash bond , a combination of Stock and cash bond by single period of the binary tree model, Derived then General Probability formula and the Derived formula of Portfolio value. then analysis the Multi-period of the binary tree model, calculating the values of Undecided rights and interests at the end of time. Finally, we used the backstepping Methods, we can get the values of the Tree Root.
keyword：bond;Option Pricing;Binary Tree Mode; Backstepping Methods;Undecided rights and interests
