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.