Geometric Brownian Motion
Overview
The geometric brownian motion is a name given to specific type of stochastic process. It is
approximated by the following equation, where S is the process being measured, and
{% \sigma %} is the volatility of the process.
{% \Delta log S = \mu \Delta t + \sigma N(0,\Delta t) %}
Here, {% N(mean, variance) %} is the normal distribution with the given mean and variance. This says the change in the
logarithm of S (the measured variable) is normally distributed.
The Geometric Brownian Motion is always positive, and has the following moments
- {% mean(log S) = \mu \Delta t %}
- {% Variance (log S) = \sigma^2 \Delta t %}
Topics
