Chapter 03 · Section 3.1

Random walk theory

The above graphic shows a random walk price evolution. Each new price shows a random differerence with the previous one. Similar models are used in physics or chemistry, e.g. for heat diffusion models or the gas theory where it is called Brownian motion. The random walk model results, among others, in a formula that describes the probability distribution as a function of time to expiration.

One can see from the three plotted distributions that the distributions become wider as time from the current date increases (from left to right), thus making prices that are far away from the starting value more likely.