Mathematical Finance Seminar

January 30, 2003 , 5:30 PM to 7:00 PM

J. Doyne Farmer, The Santa Fe Institute

Explaining the statistical properties of markets via random low-intelligence agents

We develop a microscopic statistical model for the continuous double auction under the assumption of random order flow, and test this model on data from the London Stock Exchange. We investigate the model using methods from statistical mechanics. While the predictions of the model are not perfect, they are extremely good in many respects, e.g., they explain about 70% of the variance in the daily bid-ask spread. We show that in non-dimensional coordinates the short term price impact of trading, which is closely related to supply and demand functions, approximates a universal function. New York Stock Exchange data shows similar behavior. On a broader level, this work demonstrates that stochastic models based on zero-intelligence agents are useful to probe the effect of market institutions. Like perfect rationality, a stochastic zero-intelligence model can be used to make strong predictions based on parsimonious assumptions, even if these assumptions are highly oversimplified. The standard research program in contemporary economics is to perturb equilibria based on perfect rationality, adding imperfections such as asymmetric information or bounded rationality. We propose inverting this approach, perturbing zero-intelligence models by adding a little intelligence.