Effect of Volatility and Drift on Random Walks

number of steps

volatility (resample)

maximum absolute drift(resample)

auto zoom

off

on

drift

This Demonstration generates 10 sample paths of Brownian motion with values of drift governed by a user-defined maximum absolute value. The user can vary the number of steps and volatility of the random walk. A random walk is a mathematical model for the motion of particles in suspension in a fluid. The volatility represents the temperature of the fluid and drift represents an external force applied to the particles, such as an electric field. Drift values are the same for the

x

and

y

axes, resulting in drifting directions {1,1} and {-1,1}.

The sampling occurs dynamically with the addition of new steps, i.e. if the user goes back and forth in the number of steps, the simulation will generate a different path each time.