How some economists believe that people think about the future. Nobody can predict the future perfectly; but rational expectations theory assumes that, over time, unexpected events (SHOCKS) will cancel out each other and that on average peoples expectations about the future will be accurate. This is because they form their expectations on a rational basis, using all the INFORMATION available to them optimally, and learn from their mistakes. This is in contrast to other theories of how people look ahead, such as ADAPTIVE EXPECTATIONS, in which people base their predictions on past trends and changes in trends, and BEHAVIOURAL ECONOMICS, which assumes that expectations are somewhat irrational as a result of psychological biases.

The non-Gaussian character of the marginal distribution of returns is a well-known statement in the literature. Empirical study showing that practically all financial time series exhibit a high kurtosis.

The article presents an assessment of the theory of random walks in stock market prices. In order to put the theory of random walks into perspective, two approaches to predicting stock prices are commonly espoused by market professionals. These are chartist or technical theories, and the theory of fundamental or intrinsic value analysis. Chartist theories and the theory of fundamental analysis are really the province of the market professional and to a large extent teachers of finance. Historically, however, there has been a large body of academic people, primarily economists and statisticians, who adhere to a radically different approach to market analysis, the theory of random walks in stock market prices. Random walk theorists usually stray from the premise that the major security exchanges are good examples of efficient markets. An efficient market is defined as a market where there are large numbers of rational, profit-maximizers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants.

If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.

Although general equilibrium theory originated in the late nineteenth century, modern elaboration and development of the theory began only in the 1930s and 1940s. This book focuses on the version of the theory developed in the second half of the twentieth century, referred to by Lionel McKenzie as the classical general equilibrium theory. McKenzie offers detailed and rigorous treatment of the classical model, giving step-by-step proofs of the basic theorems. In many cases he elaborates on the individual steps to give a fuller understanding of the underlying principles. His goal is to provide readers with a true mastery of the methodology so that they can derive new results that will further enrich their thinking about general equilibrium theory. Special attention is given to the McKenzie model, in which it is not assumed that the number of firms is given but rather that technologies or activities are available to any agents who can supply the resources they require. The McKenzie model is used to establish the turnpike theorems of optimal and competitive capital accumulation.

This paper presents the case for and the evidence in favour of passive investment strategies and examines the major criticisms of the technique. I conclude that the evidence strongly supports passive investment management in all markets - small-capitalisation stocks as well as large-capitalisation equities, US markets as well as international markets, and bonds as well as stocks. Recent attacks on the efficient market hypothesis do not weaken the case for indexing.

There has been little success in accounting for the absolute level of asset prices. The standard approach is that fluctuations in asset prices are attributable to changes in fundamental values. Recent studies have challenged the idea that stock price movements are wholly attributable to the arrival of news. Several tests were undertaken to determine the fraction of the variation in aggregate stock returns that can be attributed to news. First, stock returns were examined in relation to the arrival of information about macroeconomic performance. In this instance, it is shown that news proxies can explain about 1/3 of the variance in stock returns. Then, stock returns were examined in relation to other types of information. News about wars, the presidency, or significant changes in financial policies affect stock prices, but the results suggest that qualitative news does not account for all the return variation that cannot be traced to macroeconomic causes.

This paper presents evidence on the characteristic speculative dynamics of returns on stocks, bonds, foreign exchange, real estate, collectibles, and precious metals. It highlights four stylized facts. First, returns tend to be positively serially correlated at high frequency. Second, they are weakly negatively serially correlated over long horizons. Third, deviations of asset values from proxies for fundamental value have predictive power for returns. Fourth, short term interest rates are negatively correlated with excess returns on other assets. The similarity of the results across markets suggest that they may be due to inherent features of the speculative process.

This study uses laboratory experiments to determine the effects of trade and quote disclosure on market efficiency, bid-ask spreads, and trader welfare. We show that trade disclosure increases the informational efficiency of transaction prices, but also increases opening bid-ask spreads, apparently by reducing market-makers' incentives to compete for order flow. As a result, trade disclosure benefits market makers at the expense of liquidity traders and informed traders. We find that quote disclosure has no discernible effects on market performance. Overall our results demonstrate that the degree of market transparency has important effects of market equilibria and on trader and market-maker welfare.

At the most general level, behavioral finance is the study of human fallibility in competitive markets. It does not simply deal with an observation that some people are stupid, confused, or biased. This observation is uncontroversial, although understanding the precise nature of biases and confusions is an enormously difficult task. Behavioral finance goes beyond this uncontroversial observation by placing the biased, the stupid, and the confused into competitive financial markets, in which at least some arbitrageurs are fully rational. It then examines what happens to prices and other dimensions of market performance when the different types of investors trade with each other. The answer is that many interesting things do happen. In particular, financial markets in most scenarios are not expected to be efficient. Market efficiency only emerges as an extreme special case, unlikely to hold under plausible circumstances.

We report the results of 18 market experiments that were conducted in order to compare the call market, the continuous auction and the dealer market. Transaction prices in the call and continuous auction markets are much more efficient than prices in the dealer markets. The call market shows a tendency towards underreaction to new information. Execution costs are lowest in the call market and highest in the dealer market. The trading volume and Roll's (Journal of Finance (1984) 1127?1139) serial covariance estimator are inappropriate measures of execution costs in the present context. The relation between private signals, trading decisions and trading profits is analyzed.

The basic paradigm of asset pricing is in vibrant flux. The purely rational approach is being subsumed by a broader approach based upon the psychology of investors. In this approach, security expected returns are determined by both risk and misvaluation. This survey sketches a framework for understanding decision biases, evaluates the a priori arguments and the capital market evidence bearing on the importance of investor psychology for security prices, and reviews recent models.

Previous data from experiments on market entry games, N-player games where each player faces a choice between entering a market and staying out, appear inconsistent with either mixed or pure Nash equilibria. Here we show that, in this class of game, learning theory predicts sorting, that is, in the long run, agents play a pure strategy equilibrium with some agents permanently in the market, and some permanently out. We conduct experiments with a larger number of repetitions than in previous work in order to test this prediction. We find that when subjects are given minimal information, only after close to 100 periods do subjects begin to approach equilibrium. In contrast, with full information, subjects learn to play a pure strategy equilibrium relatively quickly. However, the information which permits rapid convergence, revelation of the individual play of all opponents, is not predicted to have any effect by existing models of learning.

This paper considers the relationship between agent-based modeling and economic decision-making experiments with human subjects. Both approaches exploit controlled ``laboratory'' conditions as a means of isolating the sources of aggregate phenomena. Research findings from laboratory studies of human subject behavior have inspired studies using artificial agents in ``computational laboratories'' and vice versa. In certain cases, both methods have been used to examine the same phenomenon. The focus of this paper is on the empirical validity of agent-based modeling approaches in terms of explaining data from human subject experiments. We also point out synergies between the two methodologies that have been exploited as well as promising new possibilities.

We analyze the resiliency of a pure limit order market by investigating the order flow around aggressive orders (orders that move prices). The impact of aggressive orders is gauged in two complementary ways. First, we look at the order flow before and after aggressive orders. We find strong persistence in the submission of aggressive orders. It takes about 50 subsequent orders before the order flow returns to its unconditional pattern. Second, we investigate in detail the limit order book (bid and ask prices, spreads, depth and duration) and transaction prices in a window of best limit updates and transactions around the aggressive order, respectively. We discover that aggressive orders take place when spreads and depths are relatively low, and they induce bid and ask prices to be persistently different after the shock. Depth and spread remain also higher than just before the order, but do return to their initial level 20 best limit updates before the shock. Relative to the sample average, depths stay around their mean before and after aggressive orders, whereas spreads return to their mean after about twenty best limit updates. The initial price impact of the aggressive order is partly reversed in the subsequent transactions. However, the aggressive order produces a long-term effect as prices show a tendency to return slowly to the price of the aggressive order. Finally, we find that both firm size and tick size contribute to the variation of the impact in order aggressiveness.

We perform statistical analyses of the general and sectorial historical M.I.B. indices of the Milan stock exchange. Our analyses show that the price indices have statistical properties which are compatible with a L�y random walk. The time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior. By using the theory of enhanced diffusion in L�y walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time.

We analyze statistical properties of a set of deterministic threshold elements which is introduced as a model for the stock market. The macroscopic variable of the stock market price shows seemingly stochastic fluctuation with a f^2 power spectrum consistent with real economic fluctuations. The maximum Lyapunov exponent is estimated to be zero indicating that the system is at the edge of chaos.

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between 'rational' traders whose behavior is derived from fundamental analysis of the stock, including dividends, and 'noise traders,' whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, 'bubbles' often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is large, the market price is generally locked within the price range they define.

Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including empirical statistical properties of prices, random-process models for price dynamics, agent-based modeling, and practical applications.

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Unfortunately, this model is unable to generate realistic market dynamics. The second model discards the requirement of centralized trading. Under variation of the control parameter the model exhibits two phase transitions: both a first- and a second-order (critical). The decentralized model is able to capture many of the interesting properties observed in empirical markets. Significantly, these properties only emerge when the parameters are tuned such that the model spans the critical point. This suggests that real markets may operate at or near a critical point, but is unable to explain why this should be. One of the main points of the thesis is that these empirical phenomena are not present in the stochastic driving force, but emerge endogenously from interactions between agents.

We study a generic model for self-referential behaviour in financial markets, where agents attempt to use some (possibly fictitious) causal correlations between a certain quantitative information and the price itself. This correlation is estimated using the past history itself, and is used by a fraction of agents to devise active trading strategies. The impact of these strategies on the price modify the observed correlations. A potentially unstable feedback loop appears and destabilizes the market from an efficient behaviour. For large enough feedbacks, we find a `phase transition' beyond which non trivial correlations spontaneously set in and where the market switches between two long lived states, that we call conventions. This mechanism leads to overreaction and excess volatility, which may be considerable in the convention phase. A particularly relevant case is when the source of information is the price itself. The two conventions then correspond then to either a trend following regime or to a contrarian (mean reverting) regime. We provide some empirical evidence for the existence of these conventions in real markets, that can last for several decades.

A decade ago, Sorin Solomon and Moshe Levy embarked on an interdisciplinary journey across the uncharted ocean between physics and economics. Now, 10 years on, they present a stirring account of the rich and beautiful continent they found on the way.

The study reports on the ability of competing models of market information integration and dissemination to explain the behavior of simple laboratory markets for a one-period security. Returns to the security depended upon a randomly drawn state of nature. Some agents (insiders), whose identity was unknown to other agents, knew the state before the markets opened. With replication of market conditions the predictions of a fully revealing rational-expectations model are relatively accurate. Prices adjusted immediately to near rational-expectations prices; profits of insiders were virtually indistinguishable from noninsiders; and efficiency levels converged to near 100 percent.

The idea that markets might aggregate and disseminate information and also resolve conflicts is central to the literature on decentralization (Hurwicz, 1972) and rational expectations (Lucas, 1972). We report on three series of experiments all of which were predicted to have performed identically by the theory of rational expectations. In two of the three series (one in which participants trade a complete set of Arrow-Debreu securities and a second in which all participants have identical preferences), double auction trading leads to efficient aggregation of diverse information and rational expectations equilibrium. Failure of the third series to exhibit such convergence demonstrates the importance of market institutions and trading instruments in achievement of equilibrium.

A discrete event simulation is carried out on a stock market composed of 2 kinds of participants, rebalancers and portfolio insurers. All participants have 2 kind of assets, stock and cash. Rebalancers seek to maintain some fixed proportion between the 2 assets, while portfolio insurers follow a Constant Proportion Portfolio Insurance (CPPI) rule for shifting between stock and cash. Simulation runs show how the volatility of the stock market depends on parameters such as: 1. the number of rebalancers versus CPPI investors, 2. the level of the floor that the CPPI investors seek to protect, and 3. whether the CPPI investors are permitted margin. It is found that, if margin is not used, the market is not explosive, but that the standard deviation of daily return increases manyfold as the number of CPPI investors rises from zero to 100 out of 150 investors. When 33% margin is permitted, a market with 75 CPPI investors and 75 rebalancers is explosive.

This paper reports market experiments in which human traders are replaced by 'zero-intelligence' programs that submit random bids and offers. Imposing a budget constraint (i.e., n ot permitting traders to sell below their costs or buy above their valu es) is sufficient to raise the allocative efficiency of these auctions close to 100 percent. Allocative efficiency of a double auction deri ves largely from its structure, independent of traders' motivation, intelligence, or learning. Adam Smith's invisible hand may be more powerful than some may have thought; it can generate aggregate rationality not only from individual rationality but also from individual irrationality.

We describe a model of a stockmarket in which independent adaptive agents can buy and sell stock on a central market. The overall market behavior, such as the stock price time series, is an emergent property of the agents behavior. This approach to modelling a market is contrasted with conventional rational expectations approaches. Our model does not necessarily converge to an equilibrium, and can show bubbles, crashes, and continued high trading volume.

Large distributed multiagent systems are characterized by vast numbers of agents trying to gain access to limited resources in an unpredictable environment. Agents in these systems continuously switch strategies in order to opportunistically find improvements in their utilities. We analyzed the fluctuations around equilibrium that arise from strategy switching and discovered the existence of a new phenomenon. It consists of the appearance of sudden bursts of activity that punctuate the fixed point, and is due to an effective random walk consistent with overall stability. This clustered volatility is followed by relaxation to the fixed point but with different strategy mixes from the previous one. This bursting phenomenon is the result of the system continually changing between strategy configurations that are consistent with the overall equilibrium.

A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players use a finite set of ad hoc strategies to make their decision, based on the past record. The analysing power is limited and can adapt when necessary. Interesting cooperation and competition patterns of the society seem to arise and to be responsive to the payoff function.

We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of 2=N in the N .2M region. The ability of the players to learn a given payo is also analyzed, and we show that the Darwinian evolution process tends to a self-organized state, in particular, the lifetime distribution is a power-law with exponent 2. Furthermore, we study the in uence of identical players on their gain and on the systems performance. Finally, we show that large brains always take advantage of small brains.

New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision making. Furthermore, this formulation provides the exact but novel nonlinear equations for the dynamics of the system.

A market of artificially intelligent traders is constructed to buy and sell a risky asset along with a risk free bond. Prices of the risky asset are determined endogenously from the interactions of the strategies which make trades and gather data. Each trader tries to learn about the world around it while enhancing its trading strategies. The primary purpose of this paper is to demonstrate that such a market replicates some of the basic empirical features of many asset markets including the persistence of volatility and trading volume, weak trends in prices, and leptokurtosis in returns. Also, for certain parameter values agents converge to a well defined rational expectations equilibrium.

The price fluctuations of the stocks in the financial markets are the result of the individual operations by many individual investors. However for many decades the financial theory did not use directly this microscopic representation of the markets. The main difficulties preventing this approach were solved recently with the advent of modern computer technology: massive detailed data on the individual market operations became available; microscopic simulations of the stock markets in terms of their individual participating agents allow very realistic treatment of the problem. By taking advantage of the modern computer processing and simulation techniques, we are now able to confront real market data with the results of simulating microscopic realistic models of the markets. These models have the potential to include and study the effects on the market of any desired feature in the investors behavior: departures from rationality, herding effects, heterogeneous investor-specific trading strategies. We propose to use the comparison of computer simulations of microscopic models with the actual market data in order to validate and enhance the knowledge on the financial behavior of individuals. Moreover we hope to explain, understand (and may be predict and control) macroscopic market dynamical features (e.g., cycles of booms and crashes, investors wealth distribution, market returns probability distribution etc.) based on realistic models using this knowledge.

We construct a computer simulation of a repeated double-auction market, designed to match those in experimental-market settings with human subjects, to model complex interactions among artificially-intelligent traders endowed with varying degrees of learning capabilities. In the course of six different experimental designs, we investigate a number of features of our agent-based model: the price efficiency of the market, the speed at which prices converge to the rational expectations equilibrium price, the dynamics of the distribution of wealth among the different types of AI-agents, trading volume, bid/ask spreads, and other aspects of market dynamics. We are able to replicate several endings of human-based experimental markets, however, we also and intriguing differences between agent-based and human-based experiments.

The many motivations for employing agent-based computation in the social sciences are reviewed. It is argued that there exist three distinct uses of agent modeling techniques. One such use?the simplest?is conceptually quite close to traditional simulation in operations research. This use arises when equations can be formulated that completely describe a social process, and these equations are explicitly soluble, either analytically or numerically. In the former case, the agent model is merely a tool for presenting results, while in the latter it is a novel kind of Monte Carlo analysis. A second, more commonplace usage of computational agent models arises when mathematical models can be written down but not completely solved. In this case the agent-based model can shed significant light on the solution structure, illustrate dynamical properties of the model, serve to test the dependence of results on parameters and assumptions, and be a source of counter-examples. Finally, there are important classes of problems for which writing down equations is not a useful activity. In such circumstances, resort to agent-based computational models may be the only way available to explore such processes systematically, and constitute a third distinct usage of such models.

With SUM, a Surprising (Un)realistic Market, we are dealing with the micro-foundations of a stock market. We avoid any artificially simplified solution about price formation, such as to employ an auctioneer to clear the market; on the contrary, our model produces time series of prices continuously evolving, transaction by transaction. The core of the model is represented by a computational structure that reproduces closely the behavior of the computerized book of a real stock market. The agents send to the book their buy and sell orders, with the related limit prices. The book executes immediately the orders if a counterpart is found in its log; otherwise, it records separately the buy and sell orders, to match them with future orders. The book is cleared at the beginning of each day. Our (un)realistic market emerges from the behavior of myopic agents that: (i) know only the last executed price, (ii) choose randomly the buy or sell side and (iii) fix their limit price by multiplying the previously executed price times a random coefficient. This structure generates increasing and decreasing price sequences with relevant volatility. Also bubbles and crashes appear in this market, generated within the market structure, without the need of exogenous explanations. In this framework, we then relax hypothesis (i) for a small quota of the agents, in order to investigate the consequences of the presence either of subjects using technical trading rules to forecast the future market prices and of cognitive agents capable to learn from their experience. In some way, the last ones can correspond to the artificially intelligent agents behaving as econometricians proposed by Sargent (1993). More generally, within this model we can investigate empirical puzzles that are hard to understand using the traditional representative agent structure. Among these puzzles, the time series predictability and the volatility persistence. Swarm represents for our task the correct developing framework: it provides a multilayer structure and offers the computational power needed to run the experiments for a sufficient number of cycles. Here the multilayer structure contains: (i) the observer layer, that shows the results, and (ii) the model layer, that runs either the time schedule and the environment, with the stock market (realistic) book and the (unrealistic) agents.

Microscopic Simulation (MS) uses a computer to represent and keep track of individual ('microscopic') elements in order to investigate complex systems which are analytically intractable. A methodology that was developed to solve physics problems, MS has been used to study the relation between microscopic behavior and macroscopic phenomena in systems ranging from those of atomic particles, to cars, animals, and even humans. In finance, MS can help explain, among other things, the effects of various elements of investor behavior on market dynamics and asset pricing. It is these issues in particular, and the value of an MS approach to finance in general, that are the subjects of this book. The authors not only put their work in perspective by surveying traditional economic analyses of investor behavior, but they also briefly examine the use of MS in fields other than finance. Most models in economics and finance assume that investors are rational. However, experimental studies reveal systematic deviations from rational behavior. How can we determine the effect of investors' deviations from rational behavior on asset prices and market dynamics? By using Microscopic Simulation, a methodology originally developed by physicists for the investigation of complex systems, the authors are able to relax classical assumptions about investor behavior and to model it as empirically and experimentally observed. This rounded and judicious introduction to the application of MS in finance and economics reveals that many of the empirically-observed 'puzzles' in finance can be explained by investors' quasi-rationality. Researchers use the book because it models heterogeneous investors, a group that has proven difficult to model. Being able to predict how people will invest and setting asset prices accordingly is inherently appealing, and the combination of computing power and statistical mechanics in this book makes such modeling possible. Because many finance researchers have backgrounds in physics, the material here is accessible.

In order to simulate the complex phenomena manifested in stock markets, we introduce a continuous asynchronous model in which millions of individual traders interact through a central orders matching mechanism, just as it happens in real stock markets. Each trader has a unique decision function, which allows him/her to trade at any time, to react to external news, to respond to price changes (or volume, volatility, etc.), and to consider the 'fundamental price'. As a simple example we consider three 'generic' decision functions, which correspond to three trader profiles: Noisy, Fundamentalist and Chartist.

We explore various extensions of Challet and Zhang's Minority Game in an attempt to gain insight into the dynamics underlying financial markets. First we consider a heterogeneous population where individual traders employ differing 'time horizons' when making predictions based on historical data. The resulting average winnings per trader is a highly non-linear function of the population's composition. Second, we introduce a threshold confidence level among traders below which they will not trade. This can give rise to large fluctuations in the 'volume' of market participants and the resulting market 'price'.

In this paper, an artificial financial market based on heterogeneous agents is presented. The proposed market is composed of traders with limited amount of cash, one traded asset and a centralized mechanism, the market maker, matching buy and sell orders. The price formation process is given by the intersection of the demand and the supply curve. The artificial financial market has been implemented using ad- vanced software engineering techniques, in particular extreme pro- gramming and object oriented technology. The resulting system is a powerful tool able to numerically simulate financial market operations in a realistic way. Preliminary results show that the price time series exhibits a random walk behavior with fat tails distribution of returns.

We report on a technique based on multi-agent games which has potential use in the prediction of future movements of financial time-series. A third-party game is trained on a black-box time-series, and is then run into the future to extract next-step and multi-step predictions. In addition to the possibility of identifying profit opportunities, the technique may prove useful in the development of improved risk management strategies.

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.

This brief summary provides an insider's look at the construction of the Santa Fe Artificial Stock Market (ASM) model. The perspective considers the many design questions that went into building the model from the perspective of a decade of experience with agent-based financial markets. The model is assessed based on its overall strengths and weaknesses.

We describe the main idea and the conceptual architecture of a platform for simulating a large number of asynchronously interacting agents in continuous time. We show how the generic capabilities of the platform apply to the simulation of realistic stock market interactions. A particular example of a very dramatic market event that took place in Financial Times Stock Exchange (FTSE) on September 20, 2002 is used to uncover the parameters characterizing the classical investor types within the market. The simple microscopic rules governing the individual agents behavior are shown to result in a collective market behavior similar to the one of a damped harmonic oscillator. Specifically, the aggregated influence of the fundamentalist traders is formally related to Hooke?s law while the behavior of the trend followers corresponds to inertia and viscous friction forces.

Agent-based computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents. Starting from initial conditions, specified by the modeler, the computational economy evolves over time as its constituent agents repeatedly interact with each other and learn from these interactions. ACE is therefore a bottom-up culture-dish approach to the study of economic systems. This chapter discusses the key characteristics and goals of the ACE methodology. Eight currently active research areas are highlighted for concrete illustration. Potential advantages and disadvantages of the ACE methodology are considered, along with open questions and possible directions for future research.

The origin of the universality of the stylized facts in financial markets is still a puzzle. In this paper we show analytically that a possible explanation lies in the strategies, which are commonly used by traders in every financial market, namely technical and fundamental analysis. We show that the tail index of the unconditional distribution of returns is a measure for the relative importance of these two sources of information.

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In contrast with previous MG, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. The emergent properties of the price dynamics and of the wealth of agents are strikingly different from those found in MG. As the memory of agents is increased, we find a phase transition between a self-sustained speculative phase in which a stubborn majority of agents effectively collaborate to arbitrage a market-maker for their mutual benefit and a phase where the market-maker always arbitrages the agents. A subset of agents exhibit a sustained non-equilibrium risk-return profile.

Agent-based models of financial markets traditionally adopt a discrete-time approach to represent the interactions between agents, mainly because financial time series commonly used by Economists and practitioners are available on a daily basis only. Nevertheless, one cannot discard the intraday activity, more difficult to observe but probably of importance to explain the global dynamics of the markets: new information arrives, traders update their beliefs, and prices move constantly. To address this issue, Boitout and Delahaut recently built upon an existing popular model and introduced the notion of random duration between asynchronous events. Their elegant approach, mixing discrete and continuous time, gives them a definite advantage when modeling clustered volatility in periods of intense intraday activity and allows them to compare their artificial time series with real ones.

This paper surveys research on computational agent-based models used in finance. It will concentrate on models where the use of computational tools is critical in the process of crafting models which give insights into the importance and dynamics of investor heterogeneity in many financial settings.

When they want to see how complex systems work, scientists often turn to asynchronous-time simulation, which allows processes to change sporadically over time, typically at irregular intervals. While rarely used in finance today, such models may turn out to be valuable tools for understanding how markets respond to changes in the participation rates of different types of investors, for example, or to changes in regulatory or investment policies. The asynchronous, discrete-event, stock market simulator described here allows users to create a model of the market, using their own inputs. Users can vary the numbers of investors, traders, portfolio analysts, and securities, as well as their investing and trading decision rules. Such a simulation may be able to provide a more realistic picture of complex markets.

Stock markets strive to provide an efficient trading platform for investors. Trading rules and mechanisms issued to accomplish this differ among stock markets, and are subject to modification over time. Furthermore, market participants assume a broad range of roles and trading strategies. Such variation poses problems to those involved in the study of market dynamics, when developing an artificial stock market for experimentation and analysis. More than once, the resulting artificial stock markets, and thus the experimental results, are based on very restrictive assumptions. This paper introduces an agent-based framework for artificial stock market development and experimentation. The framework is flexible in the sense that multiple market structures are supported, and an infinite range of trading strategies by market participants can be captured. Such features are accomplished through the configuration of framework properties, and the appropriate hooks for extension of the framework s components.

With a simulation study and an experimental market we explore, how valuable information in a market is. While earlier work in this field covered this question only with two levels of information we use ten different levels to control careful for the influence of additional information. We find that additional information is mostly useless and sometimes even harmful for low and medium informed investors. The second focus of the paper is to explore the usefulness of different trading strategies. Here we find that different information levels should use differing strategies, so there is no single optimal strategy.

In this paper I analyse the main strengths and weaknesses of agent-based computational models. I first describe how agent-based simulations can complement more traditional modelling techniques. Then, I rationalise the main theoretical critiques against the use of simulation, which point to the following problematic areas: (i) interpretation of the simulation dynamics, (ii) estimation of the simulation model, and (iii) generalisation of the results. I show that there exist solutions for all these issues. Along the way, I clarify some confounding differences in terminology between the computer science and the economic literature.

The computational complexity of two classes of market mechanisms is compared. First the Walrasian interpretation in which prices are centrally computed by an auctioneer. Recent results on the computational complexity are reviewed. The non-polynomial complexity of these algorithms makes Walrasian general equilibrium an implausible conception. Second, a decentralised picture of market processes is described, involving concurrent exchange within transient coalitions of agents. These processes feature price dispersion, yield allocations that are not in the core, modify the distribution of wealth, are always stable, but path-dependent. Replacing the Walrasian framing of markets requires substantial revision of conventional wisdom concerning markets.