Friday, April 24, 2009

On Stock Markets and Roller Coasters

The Economix blog offers up a simulation that alleges to show a ride on a roller coaster "whose track charts the Dow Jones industrial average from October 2007 to March 2009."

But that can't be right. Stock prices are approximately brownian motion, which means they are everywhere continuous but nowhere differentiable. In plainer English, "continuous" means that stock prices an instant from now, or an instant ago, are close to where they are now. But "not differentiable" means that the direction they move over the next instant is not necessarily close to the the direction they were heading over the last instant. A roller coaster with that property would be quite a ride.