The Predictive Power of Zero Intelligence in Financial Markets

Standard models in economics stress the role of intelligent agents who maximize utility. However, there may be situations where, for some purposes, constraints imposed by market institutions dominate intelligent agent behavior. We use data from the London Stock Exchange to test a simple model in which zero intelligence agents place orders to trade at random. The model treats the statistical mechanics of order placement, price formation, and the accumulation of revealed supply and demand within the context of the continuous double auction, and yields simple laws relating order arrival rates to statistical properties of the market. We test the validity of these laws in explaining the cross-sectional variation for eleven stocks. The model explains 96% of the variance of the bid-ask spread, and 76% of the variance of the price diffusion rate, with only one free parameter. We also study the market impact function, describing the response of quoted prices to the arrival of new orders. The non-dimensional coordinates dictated by the model approximately collapse data from different stocks onto a single curve. This work is important from a practical point of view because it demonstrates the existence of simple laws relating prices to order flows, and in a broader context, because it suggests that there are circumstances where institutions are more important than strategic considerations

How to test for partially predictable chaos

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation may split into an initial exponential decrease, characterized by the maximal Lyapunov exponent, and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and therefore remain partially predictable. Tests for distinguishing chaos from laminar flow widely use the time evolution of inter-orbital correlations as an indicator. Standard tests however yield mostly ambiguous results when it comes to distinguish partially predictable chaos and laminar flow, which are characterized respectively by attractors of fractally broadened braids and limit cycles. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories, showing that this test robustly discriminates chaos, including partially predictable chaos, from laminar flow. One can use furthermore the finite time cross-correlation of pairs of initially close trajectories to distinguish, for a complete classification, also between strong and partially predictable chaos. We are thus able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.Comment: 14 pages, 9 figure