This is true but the problem is that this model is so simple, not to say trivial, that we can use it to model almost everything. Well, I am probably too severe here, but we need a more realistic CA model to work on financial markets. I have tried to use a two-dimensional CA with three states: sell, keep or buy, and a more realistic transition rule. However, at this time, results are not very convincing from my point of view. The colored picture is a small part of a bigger image showing a typical run. One important feature of this model is the deterministic nature of its transition rule that contrast with most other studied stock market CA models. So, I hope to find something interesting the near future.
Friday, March 03, 2006
Modeling Stock Markets with Cellular Automata
In the recent years, there has been an increasing interest in simulating financial systems using multi-agent models and Cellular Automata (CA). There is a strong feeling that financial markets are typical complex systems in which the global dynamical properties mainly depend on the evolution of a large number of non-linear interacting agents. An extreme view of this is to consider that much of the randomness of financial markets is the consequence of their dynamics and has little to do with the nature or value what is being trade. This is in contrast with classical models that assume that investors are rational and consider the price a random walk. In his book "A New Kind of Science", Stephen Wolfram has proposed a very simple and idealized model of a stock market. It is a one-dimensional CA where each cell corresponds to an entity that either buys or sells on each step. The behavior of a given cell is determined by the one of its two neighbors at the preceding step (see diagrams (C) S. Wolfram). The application on this rule results in a sort of random behavior that look likes those seen on stock markets curves.