Stocks & Commodities V. 24:6 (21-30): Harnessing The (Mis)Behavior Of Markets by Rick Martinelli
Do market prices vary due to large numbers of random
effects such as the whims of individual traders?
In 1900, Louis Bachelier was awarded a doctorate from the University of Paris following his defense of a dissertation titled “Théorie de la Spéculation,” an event that marked the first time a serious academic paper addressed the behavior of the financial markets. In his dissertation, Bachelier proposed that market prices vary due to large numbers ofrandom effects, such as the whims of individual traders, and hence can be modeled as Brownian motion. Slowly, the financial community adopted his ideas, which are now the foundation of modern financial engineering.
THE BROWNIAN MODEL
Three critical assumptions underlie the Brownian
1. Price changes are statistically independent
2. Price changes are normally distributed, and
3. Price-change statistics do not vary over time.
The first assumption means that price changes behave like coin tosses, where the current change was not influenced by past changes and has no influence on future changes.
The second assumption says that the changes follow
a bell-shaped curve. This assumption is relevant
whenever random behavior is due to many small
influences. It provides a distribution function characterized by only two parameters, the mean and standard deviation, and implies a certain “contained”
behavior of the changes.