Stochastic Processes and Models

This chapter introduces the reader to definitions and key properties of stochastic processes that are important in finance. The discussion starts from the description of Brownian motion that describes the idea of a continuous random walk and proceeds to Ito processes that incorporate both trend and volatility. The emphasis of the exposition is the applicability of stochastic processes in financial modeling. The paper demonstrates that ordinary calculus cannot tackle the problems that arise in continuous time financial economics because of the presence of randomness. We offer a brief presentation of the main concepts of stochastic calculus by reviewing the Ito integral and the Ito formula. Finally, the Binomial tree model is presented as an intuitive way to approximate a stochastic process in discrete time