I understand the lognormal model etc but I was wondering where it gets the name 'geometric' brownian motion. What does it mean that the share prices tend to drift geometrically upwards? I thought that geometrically has something to do with shapes and geometry?
Hi. Thanks for your question. We don't get very many etymological queries on this forum Geometric Brownian motion is called such because from its SDE we can see that the increment (ie growth rate) is proportional to the value of the process. This results in a multiplicative rather than arithmetic increase. This can be easier to visualise in the discrete binomial model case where the share prices are the determined by repeated multiplications of u and d; geometric Brownian motion is then the limiting case of this this model. You're correct that the "geo" term relates to shapes and geometry. Historically (think ancient Greeks) multiplication problems were viewed in terms of calculating the area of shapes.
