Chapter 19

In this chapter, we begin our journey to understand models of randomly fluctuating financial variables such as stock prices or interest rates. Motivated by the discussion at the end of Chapter 17, this chapter investigates a simple prototype for randomly fluctuating returns—a random walk. We will analyze the mathematical behavior of this prototypical random system to develop some ideas about the so-called diffusion process, which we will use in Chapter 20 as the foundation for stochastic calculus and stochastic differential equations. The goal of Chapter 19 is to understand the link between the random walk and the normal distribution, and to understand the links between difference equations in two ...

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