Geometric Brownian Ito Drift
Separate a multiplicative diffusion's mean, median and logarithmic drift.
Free theory articleSeparate a multiplicative diffusion's mean, median and logarithmic drift.
Concept & interpretation
Geometric Brownian Motion (GBM) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion with drift. It is commonly used to model variables that cannot be negative, such as stock prices.
Experiment
Explore the effects of drift and volatility on the lognormal distribution of the terminal level. Open the Geometric Brownian Ito Drift module to interact with the parameters.
- Set Drift to 0.5 and observe how the Mean and Median shift to higher values. The Mean will be greater than the Median due to the right-skewness of the lognormal distribution.
- Increase the Volatility to 1. Notice how the gap between the Mean and Median widens significantly. High volatility pulls the median down relative to the mean, reflecting the negative -σ²/2 term in the log drift.
- Change the Normal coordinate to 1 or -1 to see how a typical 1-standard-deviation shock affects the Terminal level relative to the median.