This simulates the behavior of prices of stocks or other commodities, in a model sometimes called "geometric brownian motion". The transition from the price at one time to the next is

Price(t) = Price(t-1) * exp(mu + 0.5 * sigma * Z)

where mu = "drift" , sigma = "volatility" and Z is the value of a (0,1)-normal random variable. The choice of seed (and other data) completely determines the rest, so everything that happens is reproducible.

Note: There are certainly many possible variations on the formula above, and apparently varying possible conventions or usages concerning the symbols. I am told by people who know better than I that there is reason to write, instead,

Price(t) = Price(t-1) * exp((mu-sigma^2/2) + sigma * Z)
But this is not what the applet does, for better or for worse.

© 1997-2004 , Paul Garrett ... [ garrett@math.umn.edu ]
The University of Minnesota explicitly requires that I state that "The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota."