Financial prices certainly jump, skip, and leap—up and down. In fact, I contend the capacity for jumps, or discontinuity, is the principal conceptual difference between economics and classical physics. In a perfect gas, as molecules collide and exchange heat, their billions of individually infinitesimal transactions collectively produce a genuine “average” temperature, around which smooth gradients lead up or down the scale. But in a financial market, the news that impels an investor can be minor or major. His buying power can be insignificant or market-moving. His decision can be based on an instantaneous change of heart, from bull to bear and back again. The result is a far wilder distribution of price changes: not just price movements, but price dislocations.
That’s from the illustrious French American mathematician and author Benoit Mandelbrot (November 20, 1924—October 14, 2010) in his bestseller, The (Mis)Behavior of Markets: a fractal view of risk, ruin and reward (p.237).
It is important to note that a distinguished mathematician can spot the indispensable difference between ‘discontinuity’ as consequence of human action with that of the ‘averages’ as an output of natural ‘physics’ sciences.