Trading behavior and excess volatility in toy markets

We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive reactivity of agents. These issues are dealt with in detail in the simple case without public information. We also derive, for the general case, the critical learning rate above which trading behavior leads to turbulent dynamics of the market.Comment: 14 pages, 4 figures, minor change

Price fluctuations from the order book perspective - empirical facts and a simple model

Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit order sizes was found to be consistent with a power law with an exponent close to 2. A somewhat better fit to this distribution was obtained by using a log-normal distribution with an effective power law exponent equal to 2 in the middle of the observed range. The depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non-linear function of its size. A large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a short term deterministic price change, which is in accord with the law of supply and demand.Comment: To appear in proceedings of the NATO Advanced Research Workshop on Application of Physics in Economic Modelling, Prague 2001. 8 figure

Stylized facts of financial markets and market crashes in Minority Games

We present and study a Minority Game based model of a financial market where adaptive agents -- the speculators -- interact with deterministic agents -- called producers. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of active speculators grows with the amount of information that producers inject into the market. Transitions between equilibrium and out of equilibrium behavior are observed when the relative number of speculators to the complexity of information or to the number of producers are changed. When the system is out of equilibrium, stylized facts arise, such as fat tailed distribution of returns and volatility clustering. Without speculators, the price follows a random walk; this implies that stylized facts arise because of the presence of speculators. Furthermore, if speculators abandon price taking behavior, stylized facts disappear.Comment: 6 pages, 7 figure

From Minority Games to real markets

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behavior close to what is observed in real markets. In particular we find that i) fat tails and clustered volatility arise at the phase transition point and that ii) the crossover to random walk behavior of prices is a finite size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real market, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different_species_ of traders. This clarifies the nature of the interaction and the particular role played by the various populations.Comment: 9 pages, 7 figures, to appear in Quantitative Financ

Econophysics: agent-based models

This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of correlations of asset prices and returns. This second part deals with models in Econophysics from the point of view of agent-based modeling. Of the large number of multiagent- based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioral finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that we discuss extensively here. Second, kinetic theory models designed to explain certain empirical facts concerning wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.

From market games to real-world markets

This paper uses the development of multi-agent market models to present a unified approach to the joint questions of how financial market movements may be simulated, predicted, and hedged against. We examine the effect of different market clearing mechanisms and show that an out-of-equilibrium clearing process leads to dynamics that closely resemble real financial movements. We then show that replacing the `synthetic' price history used by these simulations with data taken from real financial time-series leads to the remarkable result that the agents can collectively learn to identify moments in the market where profit is attainable. We then employ the formalism of Bouchaud and Sornette in conjunction with agent based models to show that in general risk cannot be eliminated from trading with these models. We also show that, in the presence of transaction costs, the risk of option writing is greatly increased. This risk, and the costs, can however be reduced through the use of a delta-hedging strategy with modified, time-dependent volatility structure.Comment: Presented at APFA2 (Liege) July 2000. Proceedings: Eur. Phys. J. B Latex file + 10 .ps figs. [email protected]

How Market Ecology Explains Market Malfunction

Standard approaches to the theory of financial markets are based on equilibrium and efficiency. Here we develop an alternative based on concepts and methods developed by biologists, in which the wealth invested in a financial strategy is like the abundance of a species. We study a toy model of a market consisting of value investors, trend followers and noise traders. We show that the average returns of strategies are strongly density dependent, i.e. they depend on the wealth invested in each strategy at any given time. In the absence of noise the market would slowly evolve toward an efficient equilibrium, but the statistical uncertainty in profitability (which is adjusted to match real markets) makes this noisy and uncertain. Even in the long term, the market spends extended periods of time away from perfect efficiency. We show how core concepts from ecology, such as the community matrix and food webs, give insight into market behavior. The wealth dynamics of the market ecology explain how market inefficiencies spontaneously occur and gives insight into the origins of excess price volatility and deviations of prices from fundamental values.Comment: 9 pages, 5 figures, Conference on Evolutionary Models of Financial Markets, includes responses to reviewer

Expectation bubbles in a spin model of markets: Intermittency from frustration across scales

A simple spin model is studied, motivated by the dynamics of traders in a market where expectation bubbles and crashes occur. The dynamics is governed by interactions which are frustrated across different scales: While ferromagnetic couplings connect each spin to its local neighborhood, an additional coupling relates each spin to the global magnetization. This new coupling is allowed to be anti-ferromagnetic. The resulting frustration causes a metastable dynamics with intermittency and phases of chaotic dynamics. The model reproduces main observations of real economic markets as power-law distributed returns and clustered volatility.Comment: 5 pages RevTeX, 5 figures eps, revised versio

Behavior and Effects of Equity Foreign Investors on Emerging Markets

This paper analyzes empirically the behavior of foreign investors on emerging equity markets in a cross-country setting, including 14 emerging markets from the year 2000 to 2005. We could find little evidence that these investors have brought problems to local emerging markets. Foreign investors seem to build and unwind their positions on emerging stock markets slowly enough to avoid problems as price pressure or volatility and kurtosis upswings on the stock market. Also, no negative effects on the foreign exchange market could be found. Regarding feedback trading, we support two hypotheses: positive feedback trading by hedged investors and negative feedback trading by unhedged investors. The latter has stronger statistical evidence and is more likely to occur in the real world. We conclude that there is no reason to impose long-term restrictions to foreign flows.