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J Doyne Farmer

Publications and source records attributed to J Doyne Farmer.

6 recordsLinked to original sources
PubMed2005

Theory for long memory in supply and demand.

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [J.-P. Bouchaud, Y. Gefen, M. Potters, and M. Wyart, Quant. Finance 4, 176 (2004); F. Lillo and J. D. Farmer Dyn. Syst. Appl. 8, 3 (2004)]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such large orders is power-law distributed, this gives rise to power-law decaying autocorrelations in the signs of executed orders. More specifically, we show that if the cumulative distribution of large orders of volume v is proportional to v(-alpha) and the size of executed orders is constant, the autocorrelation of order signs as a function of the lag tau is asymptotically proportional to tau(-(alpha-1)). This is a long-memory process when alpha < 2. With a few caveats, this gives a good match to the data. A version of the model also shows long-memory fluctuations in order execution rates, which may be relevant for explaining the long memory of price diffusion rates.

Journal Article↗
PubMed2005

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 constraints imposed by market institutions dominate strategic agent behavior. We use data from the London Stock Exchange to test a simple model in which minimally intelligent 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 cross-sectional variation for 11 stocks. The model explains 96% of the variance of the gap between the best buying and selling prices (the 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 nondimensional 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, suggests there are circumstances where the strategic behavior of agents may be dominated by other considerations.

Journal Article↗
PubMed2003

Quantitative model of price diffusion and market friction based on trading as a mechanistic random process.

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

Journal Article↗
PubMed2002

Optimal design, robustness, and risk aversion.

Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an analytic solution for this model which explains the origin of the power laws. We also generalize the model to incorporate risk aversion, which results in truncation of the tails of the power law so that the probability of catastrophically large events is dramatically lowered, giving the system more robustness.

Journal Article↗
PubMed2002

Chaos in learning a simple two-person game.

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy.

Game Theory↗