ABSTRACT
Many fundamental concepts of stochastic calculus like filtration, conditioning, martingale, and stopping time are easy to introduce in a discrete-time setting. This chapter considers two important examples of discrete-time stochastic processes defined on the binomial sample space. The pricing of derivative securities is based on contingent claims. One needs a way to mathematically model the arriving information on which the future decisions can be based. In the binomial tree model, that information is the knowledge of all market moves between the initial and future dates. Measurability is an important concept that arises in the theory of measure and integration. In the discrete-time setting, the definition of a sub-, or super-martingale can be simplified by the tower property. Some important examples of stopping times are so-called first passage times or hitting times of a process.
