DIFFUSION PROCESSES

Diffusion processes are used to model the price movements of financial instruments. The Black–Scholes model for pricing options assumes that the underlying instrument follows a traditional diffusion process with small, continuous, random movements. Diffusion processes are usually described via partial differential equations. This makes it attractive for many discrete processes to be approximated by a diffusion process because partial differential equations are generally easier to solve than the differential‐difference equations that are often used to describe the evolution of these processes. Diffusion processes differ only in their values of the infinitesimal mean and infinitesimal variance. Brownian motion and Brownian motion with drift are examples of the diffusion process. The chapter discusses the diffusion approximation of different types of random walks such as one‐dimensional random walk, correlated random walk, symmetric two‐dimensional random walk, and Pearson random walk.