Cellular Automaton Models for Market Prices

Michael Kelly

Illinois Institute of Technology


It has long been established by Brealey and Cootner, among others, that stock prices exhibit random behavior that satisfies the Markov property of depending only upon their last values and not their previous history. This property is also consistent with the weak version of the Efficient Market Hypothesis (EMH), which asserts that the present price of a stock impounds all the information contained in its record of past prices. These two properties are consistent with models of stocks described by one-dimensional cellular automata since they also depend upon rules that describe the next state of a process in terms of the previous state without relying on past information contained in earlier times. Furthermore, the EMH implies that all the information contained in the transactions at any time can be used to construct a decision rule that will encapsulate the local behavior of all the participants in the market at that time in such a way that it completely determines the market state at the next moment. This pattern of behavior has already been observed by Wolfram in his book A New Kind of Science where he posits rule 90 as a possible model for stock prices.

In this talk we shall examine a number of one-dimensional CA and compare them with popular stock models that are contained in the financial literature. We shall attempt to discern which properties of stock behavior are best described by simple functions of CA output.