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 \mathcal{N}(0,\Delta t) %}
Here, {% \mathcal{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 essentially a Brownian Motion type process that is always positive.
Topics
- Stochastic Calculus Formulation
- Simulating Ito Time Series - shows Monte Carlo simulations of GBM's.
- Variations of GBM
- Moments of Geometric Brownian Motion