Lehrstuhl für Geld, Währung und Internationale Finanzmärkte

EU-Project: Complex Markets (completed)

Short Summary

Duration

Begin: May 2005

End: April 2008
Participating Universities
  • University of Warwick, UK
  • Abdus Salam International Center For Theoretical Physics, Trieste, Italy
  • University of Cagliari, Italy
  • University of Amsterdam, Netherlands
  • Universite Aix-Marseille, France
  • University of Kiel, Germany
Project Summary

The ability of financial markets to bear risk is central to economic welfare and stability. Growth and economic well-being is inhibited if financial markets are unable to transfer resources efficiently from the suppliers of liquidity to risk takers or entrepreneurs. Ensuring a proper return to capital and risk is the function of a market and market stability enables proper long run planning and the efficient allocation of resources to productive activities.

Despite this we are faced with levels of volatility considerably in excess of those implied by fundamentals. Markets undergo dramatic crashes and they enable speculative bubbles to develop which lead market prices away from their equilibrium values.

Classical Financial Theory, which rests on a single representative agent model of rational behaviour, has only been able to make limited progress in resolving these important practical and policy relevant issues of the apparent instability in financial markets. Therefore, the project seeks to develop an emerging alternative paradigm which explicitly emphasises the heterogeneity of the large number of micro agents within markets and allows each agent to adopt rules of behaviour that may be viewed as rational given the complexity of the market environment. Analysis of the transfer of information through the market and communication networks between the micro agents extends beyond the role played by the market price and can show how different aggregate market forms and macroscopic behaviour can evolve. Viewing financial markets as very large complex systems borrows substantial intellectual insight and method from similar systems of interacting particles in physical science. The dynamics of the aggregate market may be determined as much by the evolution of organisational form as the micro incentives. Complexity seems to be a property of economic organisation not individuals.

The proposed research seeks to analyse financial markets as complex systems of interacting heterogeneous agents using tools drawn from mathematics, physics and economics. An important element of the proposal is to incorporate within this an analysis of how human beings take decisions within complex systems of which they have a poor understanding. Hence we will also draw on behavioural motivations and psychology in order to better understand decision making under uncertainty within complex systems.

The Work Packages

Major Research Objectives
  1. The economic analysis of interaction in markets and the emergence of market networks.
  2. The analysis of complex evolutionary systems.
  3. Human decision making in complex environments: Knightian uncertainty and the use of robust decision rules by economic agents.
  4. The statistical mechanics of financial markets and systems of heterogeneous interacting agents.
  5. The relationship between the stylised empirical facts of financial markets and the scaling laws found in the mathematical physics of a large ensemble of interacting particles.
In these scientific fields, our aims are:
  • To deepen the intellectual stock of knowledge regarding the emerging alternative paradigm for understanding aggregate market behaviour in models based on heterogeneous interacting agents.
  • To deepen our understanding of human decision making in complex market environments, such as modern financial markets, where the decision environment is poorly understood by individuals.
  • To expand our ability to explain the observed empirical facts of financial markets; in particular the excess volatility, the occurrence of extreme events and market crashes, the presence of mispricing and bubbles, and the presence of herding.
  • To deepen our knowledge of how complex dynamics can arise and evolve in aggregate market behaviour from simple interactions at the micro level.
The following work packages have been designed to provide a systematic structure for the project as a whole in order address the five major research objectives above.
WP 1.1 The Economic Analysis of Interactions in Markets
WP 1.2 The Empirical and Mathematical Analysis of Market Dynamics
WP 2.1 Interaction and the Emergence of Market Networks
WP 2.2 The Foreign Exchange Market
WP 2.3 Complex Evolutionary Systems
WP 2.4 Human Decision Making in Complex Environments
WP 2.5 Statistical Mechanics of Financial Markets
WP 2.6 Stylised Empirical Facts and Scaling Laws
WP 2.7 Bubbles, Herding and Market Crashes
WP 3.1 Complexity in European Markets
WP 3.2 Policy Implications
WP 4.1 Diffusion and Dissemination
WP 4.2 Management

Packages WP 1.1, WP 2.1,WP 2.2, WP 2.7 may all be mainly associated with the first major research objective outlined above; WP 1.2 and WP 2.3 with the second, WP 2.4 with the third, WP 2.5 with the fourth, and WP 2.6 and WP 2.7 with the fifth objective. WP 3.1 and WP 3.2 are of common concern to all objectives. Finally, WP 4.1 and WP 4.2 capture the Diffusion and Dissemination and Management functions essential in order to achieve the required deliverables for the STREP as a whole and the individual research objectives. Each work package will be required to deliver state-of-the-art research in its area, as will be shown by the publication of its research in leading international journals and the acceptance and presentation of papers at international conferences.

Description of the Work Packages
WP 1.1 The Economic Analysis of Interaction in Markets

The first package is devoted to the methodological approaches and tools used to analyse markets. The different approaches will be reviewed and their strengths and weaknesses will be explored and analyzed. These investigations will enable us to draw up a theoretical framework which will serve as a reference for the empirical studies outlined below. Much of this material will reflect existing knowledge within the group since much of the literature has been created by members of this research group. However a comparative survey will present the state of the art in month 3 and will be updated as the project continues to reflect the results and insights it has gained.

WP 1.2 The Empirical and Mathematical Analysis of Market Dynamics

Work contributing to this package will be undertaken along several complementary directions. In particular, the empirical regularities and mathematical analysis of financial market data will be drawn together for comparison with the implications of the standard representative agent paradigm and the interacting agent models described in WP1.1. The evidence of simulation models will also be incorporated into this comparative survey which, will also be presented in first draft form in month 3.

WP 1.1 and 1.2 will then present evolving state-of-the art summaries of our theoretical and empirical knowledge of how financial markets function, together with a critical comparison of what each approach can and cannot explain.

WP 2.1 Interaction and the Emergence of Market Networks

Three topics will be addressed in three projects:

  • The first project is to take the wholesale fish market at Ancona in Italy for which we have data and compare the evolution of the prices on that market with those for Marseille. Ancona is organised as a three simultaneous Dutch auctions whilst Marseille is on a pairwise trading basis with no posted prices and we should be able to determine the consequences of the trading relations in the one market with their absence in the other.
  • The second project is to consider data for the Web. The standard approach is to suggest that since search is practically costless, customers will always shop around for the best deals when they are trading on the Web. Our model suggests on the contrary that individuals will tend to lock on to their suppliers and this even when the best deals are not provided by that supplier. This has very important consequences for the behaviour of suppliers and may lead them to charge higher prices to their loyal customers. This will require obtaining data on individual behaviour and will necessitate recovering information obtained from "cookies" and we will collaborate on this with Mark Newman at the University of Michigan who is used to handling this sort of data.
  • The third project is to analyse the data from the Marseille fruit and vegetable market where we have details not only of transaction prices but also of the offers and counter-offers both in the case where there was a transaction and in the case where the negotiation was broken off. Our aim is to determine the effect of the bargaining on the final price. A first paper on this subject is to appear in Journal of Economic Behaviour and Organisation.
WP 2.2 The Foreign Exchange Market

This part of the project is to test the approaches developed in WP2.1 on the Forex market in London and Paris. Alan Kirman developed a number of contacts at the largest banks whilst holding a Houblon Norman Fellowship at the Bank of England and the idea would be to look at the extent to which traders tend to trade with a small group of other traders rather than take the apparently best deals available on the screens. This approach has been adopted by Baker (1984) in his study of a major securities exchange and by Abolafia (1996) in his analysis of the Chicago Commodities Exchange. What Baker shows is that the volatility of options prices is dependent on the type of network structure in a market. Once again our idea is to examine the extent and consequences of the existence of networks in such apparently large and anonymous markets. Our idea is also to compare the evolution of prices in such a market with an electronically organised order book such as the Paris Bourse where we can obtain data thanks to the COB, the Commission des Operations de la Bourse (now become the Autorité des Marchés Financiers, where Alan Kirman is a member of the scientific advisory board). We also intend to pursue the analysis of the impact of interaction and resultant changes of opinion in financial markets. With Hans Follmer and Ulrich Horst from the mathematics department of the Humboldt University in Berlin we wish to continue trying to characterise the sort of stochastic process that leads to bubbles and crashes. This will involve a more realistic notion of equilibrium than those used currently in the literature.

The analysis of the foreign exchange market will also form the empirical basis for that part of the research programme considering robust rules of behaviour and decision making under Knightian uncertainty. The work will involve the development and rationalisation of behavioural strategies based on input from behavioural psychology and the analysis of transaction level data in foreign exchange markets and interviews. We need to understand the rules of thumb adopted by forex traders when the market is under stress.

WP 2.3 Complex Evolutionary Systems

Economics is witnessing an important paradigm shift, from a representative, perfectly rational agent modeling approach towards an interacting multi-agent approach with heterogeneous boundedly rational agents (see for example Kirman (1992) for a critique on representative agent modeling).

The goal of this research package is to study complex evolutionary systems ranging from large computer simulated systems (e.g. Arthur et al. (1997a), LeBaron et al. (1999), Lux and Marchesi (1999)) to small, analytically tractable evolutionary systems (e.g. Brock and Hommes (1997, 1998), Lux (1995, 1997)) and to test the relevance of the evolutionary approach in laboratory experiments and empirically. A good feature of the representative rational agent hypothesis is that it puts natural discipline on agents' forecasting rules and strategies, and minimizes the number of free parameters in the models. In contrast, the "wilderness of bounded rationality" leaves too many degrees of freedom in modeling, and it is far from clear which habitual rules of thumb out of a large class are most reasonable. Stated differently in a popular phrase: "there is only one way (or perhaps a few ways) one can be right, but there are many ways one can be wrong". The philosophy underlying the evolutionary approach is to use simple forecasting rules based upon their performance in the recent past, so that "evolution decides who is right".

In a complex evolutionary system strategies, ranging from fairly simple to rather sophisticated, compete against each other. Agents can switch between different strategies and tend to employ strategies that have performed well in the recent past. This research program aims at a systematic investigation of complex evolutionary systems from a theoretical, computational, experimental as well as an empirical viewpoint. Key questions that need to be addressed in the complex evolutionary approach include the following:

  1. Which strategies survive evolutionary competition?
  2. What is the simplest, to some extent analytically tractable simplified evolutionary system that can mimic observed behavior in large evolutionary systems?
  3. Which evolutionary systems can explain observed laboratory experiments?
  4. Which evolutionary systems can be calibrated or estimated from real financial or economic data?

The first research question relates to a long lasting debate among economists, dating back to Friedman (1953), who argued that non-rational agents will be driven out of the market by rational agents, who will trade against them and simply earn higher profits. In recent years however, this view has been challenged and heterogeneous agent models are becoming increasingly popular, especially in financial market modeling. Two typical traders types arising in many heterogeneous agent financial market models are fundamentalists and chartist or technical traders. Fundamentalists base their investment decisions upon market fundamentals such as dividends, earnings, interest rates or growth indicators. In contrast, technical traders pay no attention to economic fundamentals but look for regular patterns in past prices and base their investment decision upon simple trend following trading rules. Computer simulations such as those of the Santa Fe artificial stock market (LeBaron et al. (1999), but see also e.g. Kirman (1991), Lux and Marchesi (1999, 2000), Marsili et al. 2000, 2001) have shown that rational, fundamental traders do not necessarily drive out technical analysts, who may earn higher profits in certain periods. An evolutionary competition between these different trader types, where traders tend to follow strategies that have performed well in the recent past, may lead to irregular switching between the different strategies and result in complicated, irregular asset price fluctuations. Brock and Hommes (1997, 1998) have show in simple, tractable evolutionary systems that rational agents and/or fundamental traders do not necessarily drive out all other trader types, but that the market may be characterized by perpetual evolutionary switching between competing trading strategies. Non-rational traders may survive evolutionary competition in the market (see for example, Hommes (2001) for a survey).

Approximating large, complex evolutionary systems
Many heterogeneous agent models are artificial, computer simulated markets. This work views the economy as a complex evolving system composed of many different, boundedly rational, interacting traders, with strategies, expectations and realizations co-evolving over time (see for example, work at the Santa Fe Institute collected in Anderson et al. (1988) and Arthur et al. (1997). Several researchers (e.g. Lux and Marchesi (1999), Challet et al. (2001), Kirman and Teyssiere (2001)) show that these type of interacting agent models are able to generate many of the stylized facts, such as unpredictable returns, clustered volatility, fat tails and long memory, observed in real financial markets. Gaunersdorfer et al. (2000) have studied simple, analytically tractable 2-type evolutionary systems able to generate some of these stylized facts. Manzan (2003) recently estimated a simple evolutionary 2-type heterogeneous agent model on the S&P 500 index and found evidence for heterogeneity, with one stabilizing fundamental type and one destabilizing trend following type. Estimation of heterogeneous agent systems is still in its infancy however, but joining the multi-disciplinary expertise in the proposed network may trigger significant progress to address this important problem.

Large, complex systems have many degrees of freedom, and it is difficult what exactly drives the good simulation results. In statistical mechanics methods to deal with large interacting particle systems have been developed. In economics, relatively little theoretical work has been done on the study of large evolutionary systems. In a recent paper, Brock, Hommes and Wagener (2004) developed the notion of a Large Type Limit (LTL). A LTL is a (low-dimensional) approximation of a very large complex system. As an example, consider a financial market with heterogeneous agents using many different trading strategies. Strategies are simple forecasting rules, with random parameters drawn from a common distribution. The LTL approximation is obtained by replacing sample moments in the heterogeneous market equilibrium equation by population moments. BHW show that a large complex system is well approximated by its LTL. They also show that, as agents become more sensitive to differences in evolutionary fitness, an LTL becomes dynamically unstable and complicated endogenous asset price fluctuations arise. This shows that in a large complex system the law of large numbers breaks down when evolutionary pressure is sufficiently large. Asset prices can then persistently deviate from the economic fundamental benchmark and the asset can exhibit persistent over- or under-valuation and temporary speculative bubbles. Diks and van der Weide (2004) have recently generalized the notion of LTL to Continuous Belief System (CBS), where asset prices and a continuous distribution of beliefs or strategies adopted by the population of traders co-evolve over time. Under suitable regularity conditions the evolution of the distribution of beliefs is completely determined by the evolution of the lower order moments, such as the mean and the variance, over time. A promising approach seems to apply these recently developed notions of LTL and CBS to other interacting agent models developed by other network participants. An important goal is to estimate an LTL and/or a CBS on economic and financial data and estimate "the degree of heterogeneity" in the real economic and financial data.

Laboratory testing of evolutionary systems
In the last decades laboratory experiments in economics have become a recognized tool for testing economic theories, as e.g. illustrated by the 2002 Nobel Prize in Economic Science for Daniel Kahneman and Vernon Smith. In a famous experiment, Smith et al. (1988) observed bubbles and crashes in experimental asset markets. These experiments show that in a controlled laboratory environment asset price may deviate substantially and persistently from their rational expectations fundamental value. In a recent series of laboratory experiments in commodity as well as asset markets Hommes at al. (2002a, b, c) have investigated under which circumstances participants can learn to coordinate on the fundamental price and under which circumstances participants may coordinate on (temporary) bubbles. An important topic for future work is to calibrate or even estimate an evolutionary switching model on laboratory data.

Relevance to other fields
Complex evolutionary systems and its approximations may be viewed as simple stylized models of behavioral economics and behavioral finance. Agents select simple strategies from a class of habitual rules of thumb. In such a world, agents are not fully rational, but it is important to stress that agents are also not irrational, but boundedly rational, since they tend to select rules that have performed well in the recent past. The behavioral approach is becoming increasingly popular in economics and finance. A multi-disciplinary approach, with interaction between economics, finance, psychology, experimental economics and physics will be extremely fruitful.

From a mathematical viewpoint, bifurcation theory and nonlinear dynamics play an important role in this research. A LTL or a CBS is a (low-dimensional) nonlinear system possibly buffeted with (small) noise. In the case without noise, several bifurcations, such as Hopf-bifurcations, pitchfork bifurcations and routes to chaos, have already been detected. The proposed research aims at studying bifurcation phenomena in the presence of small noise and in particular study the statistical time series properties. Stochastic bifurcation theory will play an important role. We intend to study bifurcations in stochastic systems, starting and motivated by simple LTL's and other heterogeneous agent systems in economics and finance. A key question is whether these simple systems buffeted with noise can generate all "stylized facts" observed in real financial data.

Mathematical and statistical tools as well as computational tools will be used extensively in this research project. It is a multi-disciplinary project, which is important for economics and finance, but also for mathematics and statistics.

WP 2.4 Human Decision making in Complex Environments

We need to explore how agents in markets actually take decisions rather than how financial theory and economists feel optimising and fully rational decisions should be made. The distinction lies in the presumed form of optimality and rationality associated with agents. The project outlined immediately above has briefly discussed the evolutionary selection of decision rules and in this project we want to explore the theoretical basis of robust rules of thumb and their evolutionary potential.

Human cognition is, of course, adapted to deal with a highly complex physical and social environment. The perceptuo-motor systems, and systems for commonsense and social reasoning are highly sophisticated, and are able to integrate enormous amounts of information very rapidly and effectively. By contrast, though, human decision making with numerical or financial decision-making problems is strikingly limited. In a wide range of judgement problems, for example, from personnel selection to medical diagnosis, people are typically equally or outperformed by simple linear regression or simpler methods (Dawes; Gigerenzer). Moreover, people exhibit large and systematic biases in dealing with complex decisions - indeed, even trading off between two or more factors in a decision about, for example, risk and return, seems to overload the cognitive system (Stewart, Chater, Stott & Reimers, in press).

In the abstract world of economic and financial decision making, then, it seems that people are quite poorly equipped to deal with complexity. Indeed, studies of how people learn to make new kinds of relatively complex decision (e.g., Payne, Bettman & Johnson) have shown that people use very simple heuristic strategies, to deal with complex environments. Indeed, it seems likely that the more complex the decision environment, the simpler the strategies people are likely to use---essentially because the problem of developing successful sophisticated strategies may be too difficult in a complex environment. There is an interesting potential parallel here with the formal sophistication of scientific theories, which is greatest when dealing with very simple phenomena (e.g., elementary particles), and least when dealing with complex phenomena (such as societies).

Major developments have taken place over the last ten years in the control engineering literature with the extraordinary growth in what is known as H-infinity theory. Essentially this approach adopts a min-max strategy familiar in economics (see Gilboa I. and D. Schmeidler, (1989)) in that decision makers consider the best action they can take given a worse case environment. This worse case need not be dramatically bad but is defined by a set of potential alternative environments. This description of the uncertainty can then be deterministic and not stochastic and as such represents a new way in which robust decision rules can be constructed in the face of uncertainty.

We should make a distinction between "Risk" and "Uncertainty" where Risk describes the case where economic agents have the ability to construct probability distributions that describe the unknown elements of their decision environment. Uncertainty as stressed by Knight (1921), or Knightian Uncertainty, describes a situation where for many distinct potential reasons we cannot rely on this standard probabilistic structure. For instance we may be faced with "one off" events for which we have no prior experience and hence no formal basis to construct probabilities or subjective information that could help in forming "rational" or optimal decisions. Alternatively we may be uncertain about our assumed probabilistic structure itself. We may be unsure as to whether to use one probability distribution or another to describe our uncertainty. This in effect translates to the agent being faced with several different potential models of the environment when constructing decisions.

Standard finance theory has obviously emphasised risk and a stochastic approach to uncertainty. This leads to the representative agent taking decisions on the basis of an assumed probability distribution which is supposed to accurately describe the uncertainty in the market. However this approach has led to a range of "anomalies" that financial theory cannot explain within the rational representative agent paradigm, such as the equity premium puzzle in which unrealistic levels of risk aversion are required to account for the observed differential returns on equities and bonds.

  • In this project we wish to explore the role of Knightian uncertainty and model risk in the formation of financial decisions by micro agents and their impact on aggregate dynamics.

One way to view this issue is that standard theory assumes that there is one source of uncertainty, market risk but it does not allow the models that economic agents use to be misspecified. Given the complexity of the market we will not assume that agents have the ability to form fully rational decisions, which implies full knowledge of the market but instead assume that notion of rationality adopted is one which implies that agents form and use decision rules that are robust to misspecification. The robust rules constructed using H-infinity theory can be shown to be effectively equivalent to those that those that follow from recognising Knightian uncertainty. A special issue of the Journal Macroeconomic Dynamics, edited by Mark Salmon has recently appeared (February 2002) in which initial work on developing this new framework has been presented.

We also wish to integrate theoretical insights gained from the Human Decision making and Psychology with our analysis of market behaviour. We need to understand how individuals faced with a complex partially understood environment will respond; what rules of thumb they might adopt and whether these can be seen to be robust and what impact the use of such rules of thumb will have on aggregate market dynamics. To this end we can see the following research plan:-

  • Some interview work within City Institutions will be required in order to investigate the nature of "the rules of thumb" using by traders and then we need to assess how they correspond to standard fully rational rules and robust decision rules. We want to explore the relationship between robustness and the evolutionary selection of rules of thumb and the psychological behavioural constraints on decision making. The idea here is to evaluate theoretical models in which agents use simple "rules of thumb" but where, importantly agents select among the rules available to them according either to their success or some psychological or behavioural motive.. This sort of idea has already been applied to the way in which agents forecast future prices in financial markets and can explain the large swings of opinion and "bubbles" observed on such markets
  • A second stage would be to examine the interaction between agents who employ robust rules in financial markets. This would involve considering some explicit strategic interaction in a foreign exchange market microstructure setting. How does robustness interact with a tendency to herd for instance? (See Hwang and Salmon 2004)
  • We also wish to examine how uncertainty about equilibrium prices affects and limits the forces of arbitrage in financial markets and hence allows bubbles to be created.
  • We need to explore the impact of model risk and model misspecification on pricing.
  • Finally we want to examine the impact on the aggregate dynamics of the market if a large number of agents are using robust decision rules and secondly mispecified models and decision rules. Does the adoption of robust pricing lead to greater volatility - does it allow the growth of bubbles?
WP 2.5 Statistical Mechanics of Financial Markets

The empirical evidence depicts financial markets as complex self-organizing critical systems. Indeed the statistics of real market returns deviate considerably from the Gaussian world predicted by Bachelier at the turn of last century. Rather Mandelbrot observed that fractal (Levy) processes provide a closer approximation, even though that seems not to be an entirely satisfactory model. Market returns display scaling, long range volatility and there is evidence of multiscaling. Such features evoke the theory of critical phenomena in physics, which explains how such features emerge from the interaction of many microscopic degrees of freedom and statistical laws. Financial markets are systems of many interacting degrees of freedom (the traders) and there are very good theoretical reasons to expect that they operate rather close to criticality. These expectations have been substantiated by microscopic agent based market models (see Berg ,et al (2001) Challet D, Marsili M, Zhang YC (2001a,b)). These models belong to a strand of literature which differs from that of the numerical simulation of agent based models. This strand originated from the Arthur's El Farol bar problem and its later variant - the Minority Game by Challet & Zhang. These models try to capture the essence of agent-agent interaction while preserving a full heterogeneity in strategy space. It was later realized that the stationary state of these models could be characterised exactly using sophisticated methods of statistical mechanics of disordered systems (see Marsili M, Challet D (2001),Marsili M, Challet D, Zecchina R (2000), Challet D, Marsili M, Zecchina R (2000)). This has provided a deep understanding of the self-organization that takes place in these models. The picture offered by these synthetic markets is one where speculation drives markets towards information efficiency - i.e. to a point where market returns are unpredictable. But the point where markets become exactly efficient is the locus of a phase transition. Close to the phase transition the behavior of synthetic markets is characterised by the observed stylized facts - fat tails and long range correlation -whereas far from the critical region the market is well described in terms of random walks. While there is a suatisfactory understanding of the overall picture (Challet D, Marsili (2003)) precise quantitative analysis of the anomalous fluctuations at the critical point have not been carried out yet. Very powerful techniques of statistical mechanics, such as the Renormalization Group, could be adapted to the problem in this respect.

Modelling and empirical analysis have been mostly confined to single assets or indices. Recently ensembles of assets and their correlation have become the focus of quite intense interest. Giada and Marsili M (2001) recently applied a new data clustering approach and derived results that strongly support and extend the view of a self-organized critical market. We show that long range correlation and scale invariance extends both across assets and, in the behavior of the ensemble of assets, across frequencies. More precisely, we uncover the internal structure of correlation both across different assets and across different days. We identify statistically significant classifications of assets in correlated sectors and of daily profiles of market-wide activity in market states. Both the statistics of sector sizes and of state sizes show scale free properties.

Determining market's states is an important achievement both theoretically and practically: The concept of a state which codifies all relevant economic information is the basis of many theoretical models of financial markets. In everyday life, traders are flooded with massive flows of information and data compression and mining are crucial issues.

The same techniques used to deal with heterogeneous traders can also be used to deal with heterogeneity in general socio-economic problems. The spirit is the same as that which led E.P. Wigner to apply random matrix theory to the spectral properties of large nuclei: When one deals with a large system with a complicated structure of interactions, it makes sense to assume that collective properties will not be too sensitive to micro details, and hence that a system with random interactions can exhibit a similar behavior. We recently undertook the study of the typical properties of the competitive equilibria of large random economies. Specifically we studied a simple model with linear activities but we plan to extend this approach to other, more realistic systems. In doing that the interaction with economists is of utmost importance.

The specific objectives of this project are:
  • To push further our understanding of theoretical models of heterogeneous interacting agents in financial markets, specially in the high volatility phase, drawing on the theory of statistical mechanics. In particular we plan to apply the Renormalization Group transformation to clarify the critical properties of the simple models.
  • To develop multi-asset models of financial markets and multi-market models that can explain the multivariate structure of correlation on different assets.
  • To extend the use of techniques of disordered statistical mechanics to further soci-economic problems
WP 2.6 Stylised Empirical Facts and Scaling Laws

Practically all financial markets (stock markets and foreign exchange markets as well as derivative markets) share the same pervasive stylised facts; amongst these are a unit root in asset prices, leptokurtosis in returns, a power-law distribution for extreme returns, i.e. a simple relationship like , with the so-called "tail index" hovering around 3; and volatility clustering. Another closely related recent development is the finding that financial prices exhibit the signature of multi-fractality which shows up in different degrees of long-term dependence in various transformations of financial data (raw, absolute or squared returns), cf. Mandelbrot et al. (1997). As shown in Lux (2001,2003), so-called multi-fractal processes from the statistical physics literature, originally designed as a stochastic model for turbulent fluids, provide a remarkably accurate description of the volatility dynamics of financial markets and seem to have great promise as a new tool in financial econometrics.

A theoretical explanation is required for these common stylised facts. The efficient markets hypothesis (EMH), which has for a long time been the only theoretical framework within which to consider these stylised facts rests on a full reflection of information within market prices and hence the efficient distribution of news. Although news is of paramount importance in financial markets, the EMH is unsatisfactory in that it defers the explanation of the stylised facts to largely exogenous forces (the news) and moreover this cannot be easily tested since much of the news arrival process is not directly observable.

An alternative explanation is that the stylised facts have their origin, at least in part, in the trading process with its interaction of a large ensemble of heterogeneous traders rather than in extraneous information events. Market crashes do occur for instance when there has been little or no apparent news arriving on the market. Market sentiment somehow changes spontaneously. The global market crash in 1987 is often cited as an example of this sort of event. The perplexing similarity of the statistical characteristics of very different markets could, then, be explained, by the similarity of the behaviour of traders and market interaction regardless of the asset involved. Alan Kirman proposed an interacting agent model of foreign exchange market speculation with interpersonal links (Kirman, 1991, 1993). While his focus at that time was on the potential explanation of speculative bubbles and crashes through herding and contagion, recent variants of the model have been shown to give rise to some realistic scaling properties (Kirman and Teyssiere, 2001). Lux (1995) is concerned with the emergence of speculative bubbles and their subsequent collapse in models of speculative activity. These phenomena are described as emergent macroscopic properties from the microscopic interactions of a large ensemble of autonomous traders and the paper uses analytical tools from statistical physics (mean-field approximations, Master equation framework) to tackle the resulting complex dynamics. Later extensions of this framework, showed that variants of the model were able to explain the excess kurtosis of financial returns (Lux, 1998) and could provide an avenue for the explanation of time-varying volatility (Lux, 1997). A fully worked out perspective on the potential explanation of a whole set of empirical scaling laws through interacting agent models appeared in an article published in Nature (cf. Lux and Marchesi, 1999) and subsequent elaborations on this topic can be found in (Lux and Marchesi, 2000; and Chen, Lux and Marchesi, 2001).

Identifying the interaction between different types of traders such as rational optimising agents and positive feedback traders can account for the excess volatility of financial prices compared to that implied by fundamentals. The models of Kirman (1993), Lux and Marchesi (1999) and Brock and Hommes (1998) distinguish between fundamentalists and chartists and go beyond the noise trader literature by treating agents’ behaviour in a probabilistic manner. As a basic ingredient in these models, market participants are allowed to switch between behavioural alternatives with certain probabilities. The later are, however, not given exogenously, but depend on the state of the market as well as interactions which introduces potential herding and contagion effects. With a large ensemble of traders exerting an influence on each other, a relatively complex picture of the functioning of the market emerges.

Although some basic insights into the working of such "artificial" markets can be obtained theoretically, the more important results can only be obtained through numerical simulation. Keeping track of the decisions of each individual investor, the Lux-Marchesi model is an agent-based approach which derives the overall (macroscopic) features of the market as emergent phenomena from the microscopic interactions of the agents. All the major stylised facts emerged from the market process itself in their simulations even though they were absent from the statistical model used to generate the fundamental news. For example, even with news about fundamentals following a Normal distribution, we found that the distribution of changes of the market price was characterized by a high number of extraordinarily large (positive or negative) observations as well as by alternations between periods of high and low volatility. Hence, the major features of observed returns were found in the time series generated by the artificial market. This implies that the trading process acts like a noise magnification mechanism which transforms white input noise into a much more complicated process for the asset price series.

The explanation of empirical laws through the collective behaviour of interacting units is a familiar story to physicists. Financial returns exhibit characteristics that resemble so-called scaling laws for physical systems which are recognised to be the outcome of systems of a large ensemble of interacting particles.

An important aspect of the proposed research of the project is that we plan to extend the scope of questions treated with the help of the microscopic simulation approach. Available literature has so far been mainly concerned with the explanation of the stylised facts reviewed above. While this constituted one of the main motivations for the invention of this strand of literature, its success in shedding light on these formerly mysterious facts also justifies its application to a wider scale of economic problems. In particular, we plan to deal with the following topics:

  • the importance of various institutional arrangements and regulations,
  • the mutual influence between short-term speculative activity and long-term investments (long-term capital movements in foreign exchange markets),
  • the analysis of speculative attacks within systems of pegged exchange rates or currency bands.

The similarity of the statistical results across different markets is the more astonishing as the details of the trading process and market organization do differ enormously. This holds when comparing the institutions of various national stock markets for which a variety of market-clearing processes (like continuous auctions, market maker systems etc.) have been designed. The most remarkable differences exist, however, between the organization of stock markets, on the one hand, and the world-wide market for foreign currencies, on the other hand. The latter is characterized by a particular multi-layer structure with major banks acting as market makers for their customers, but trade between banks accounting itself for a large fraction of the overall trading volume.
Our research interests here are twofold: first, by taking into account various institutional details of real-life markets, we attempt to explore the robustness of the emergence of typical statistical features that have been found in our simpler models. In this way, we hope to get evidence on one of the deepest questions in this research project: developing multi-agent models with different institutional details, we are curious whether human multi-agent systems share the same lack of sensitivity with respect to microscopic details that characterizes physical multi-particle systems. The "microscopic details" in our case are the details of the market organization which will be varied in the course of our exploration. As outlined above, the statistical facts do strongly support the idea that there are some overall regularities which work in the same way in various markets. If we could find similar behaviour with experiments of a series of virtual markets with different styles of market organization, this would lend strong support to the hypothesis of universal factors in human behaviour as the ultimate origin of some of the stylised facts.

The second motive for developing a number of specialized models (with particular emphasis on the case of the forex market) is more mundane, but probably not less important: from a policy viewpoint, foreign exchange markets have attracted particular attention in recent years and we hope to contribute significantly to these issues with a refined microscopic model of the market for foreign currency. The following points give a detailed accounts of the questions we plan to deal with and the potential advantages of our approach in their treatment.

In asset markets as well as in foreign exchange markets, speculators are not the only group of market participants. In all financial markets we have to take into account additional long-term investors whose economic welfare may be affected by the presence of speculators.

  • The question, then, is whether international trade and long-term capital movements are distorted by excessive speculative activity.

Although this is an issue of paramount importance and measures to "throw sands into the wheels of international finance" by means of levying taxes on speculative transactions (Tobin-taxes) or capital controls are hotly debated, the theoretical arguments are far from being settled. In fact, theoretical models on excessive speculation and imposition of regulatory measures are astonishingly sparse in economics literature (exceptions are to be found in Ul Haq et al., 1996). The reason for this neglect is again the complexity of possible reactions of market participants: they may not only react with a gradual change of their activity, but may rather switch to a totally different strategy. In a setting with given structural relationships between macro variables, such "deep" behavioural changes are out of reach (in economics, this well-known problem in the analysis of policy measures is termed the "Lucas critique"). The multi-agent approach, on the other hand, with the possibility of agents' adaptively altering their behaviour provides an avenue for taking such effects into account. Given the importance of the questions of regulating or not international financial markets, our research here will focus on a thorough analysis of the impact of measures like the Tobin tax.

A related policy issue is the usefulness of pegged exchange rates or currency bands (as they have been in use in Europe before the introduction of the Euro). In economic theory, it is well known, that, on one hand, the commitment of the government (or central bank) to defend the peg works as a stabilizing factor not only directly by keeping exchange rate fluctuations in check, but also indirectly through the expectations of market participants (Krugman, 1991; Krugman and Miller, 1993). On the other hand, the possible uncertainty about the feasibility of the peg under adverse developments creates an incentive for speculators to attack the peg via massive sales of the weak currency. It is important to notice that this phenomenon is quite different from the behaviour underlying speculative behaviour in markets with freely floating prices. The past decade has experienced a number of spectacular attacks, most notably those that led to the EMU crisis in 1992/93. More recently, this phenomenon has also plaid a major role in the Asian crisis, with both examples of successful and more recently (Taiwan, Hong Kong) also unsuccessful attempts to urge the central bank to abandon its exchange rate policy.

Available models of this phenomenon are of a static, game-theoretic nature throughout. However, due to their mode of construction, they leave open a number of relevant issues. First, most models have a continuum of solutions so that they do not allow to predict when exactly a speculative attack will occur in real-life markets. Second, all speculative attacks are successful in this framework, while experience shows that unsuccessful attacks occur as well. Again, it seems that what is missing from the current literature is dynamics and interaction of market participants. In our view, the framework developed in our multi-agent models appears well suited to add important insights to this branch of literature as well. First, in order to better understand the operation of the market in the course of speculative attacks, the collective actions and co-ordination among speculators themselves have to be analysed in a dynamic setting with heterogeneous agents. Second, the interaction of speculators with other groups of traders also deserves an in-depth analysis.

In the pursuit of these topics, our aim is to continue the tradition of the earlier work in that we attempt a synthesis of both theory and computer simulation. Key features of the models to be developed should be subject to economic reasoning, while additional insights on emergent behaviour could be achieved by massive computer simulations.

WP 2.7 Bubbles, Herding and Market Crashes

This work package will draw together as a common theme research which will have been considered in the various work programmes on the major market "failures" In particular it will address how the preceding theoretical and empirical analyses of behaviour in complex markets can aid our understanding of Bubbles, Herding and Market Crashes. In this case we will use data drawn from equity and foreign exchange markets for subsequent comparison with US market failures. Work will focus on

  • the role of Bayesian Learning in financial markets and
  • the empirical estimation of agent based models
  • In particular we will analyse, from an agent based perspective, episodes of speculative attack and market crashes.
WP 3.1 Complexity in European Markets

The third section, which is subdivided into two work packages 3.1 and 3.2, will present the general policy conclusions to be drawn from the studies outlined above.

The first, package will be based on the results of the empirical studies, from which it will draw conclusions from a comparative analysis of markets within the European Union and North America from a complexity point of view. Different forms of behaviour following from different socio-economic dynamics may be at work in different markets given different market organization and forms. Day trading is much more prevalent in the US for instance. Is complexity equally prevalent in all markets? Reflection on this point will be conducted throughout the duration of the research, ensuring that these concerns are taken fully into account in the WPs. During the final twelve months, when sufficient empirical data has been gathered, a special team charged with the task of drawing up a report on this theme will be set up, under the direction of the Coordinator.

WP 3.2 Policy Implications

The second work package within the third section is directly linked to the preceding two work packages and the work will be carried out concomitantly. In particular, we will analyse in general how policy, eg. Tobin taxes, may be implemented to inhibit asset price volatility.

WP 4.1 Diffusion and Dissemination

The fourth and final section is central to the proper management and organization of the project as a whole and each of the foregoing WPs. Package 4.1, as its name suggests, is dedicated to the diffusion and dissemination of the results, both within the Consortium and, when appropriate, externally. All partners will be involved in some part with both internal and external diffusion and dissemination. In addition to the website, which will serve as an instrument of exchange and coordination throughout the duration of the project, we plan to organize two events towards the end of the project (between months 34 and 36), with the aim of diffusing our results externally and enhancing their value: i) an International Workshop, to which also non-European experts from both academic and professional fields will be invited as "commentators"; ii) one (or two) Round Tables aimed at the European policy and business communities. An important element in this WP will involve the targeting of SME's and the transfer of the results obtained within the STREP to market practitioners.

WP 4.2 Management

Is dedicated to tasks specified under the 6FP call that include the coordination of audit certificates, the maintenance of the consortium agreement, managing the central finances of the project, the overall legal, contractual, ethical, financial and administrative management, the coordination of the knowledge management, implementing competitive calls for the potential participation of new contractors and the coordination of the technical activities of the project.

Monitoring and Accountability

A continuous monitoring process will be put in place so that the lead co-ordinators of the individual work packages report to the co-ordinator of the project as a whole as to progress of research in the related work package. This will enable any specific risks to be identified, such as the poor performance of an individual researcher, and suitable action to be taken.

The resources required to carry out this research programme have been detailed below and when mobilised with the resources already available at the host institutions will be sufficient to achieve the stated objectives.

Success in achieving the objectives will be measured by the ability of the lead coordinators of the individual work packages in being able to deliver the required research reports according to the required time scale for presentation to the consortium meetings as outlined in the work plan in section 7 below. These goals effectively translate the objectives into deliverables that can be monitored. Aside from the main reports each work package will naturally develop a range of research papers that will be made available on the web site. Any work package that does not develop a strong set of ancillary scientific research reports will prove to be unsuccessful. Similarly success will be monitored by the presentation of research based on the project at external scientific meetings and conferences.

The set of major research issues addressed within this set of inter-linked work packages all revolve around the major interdisciplinary theme of complexity in markets and human decision making in complex and poorly understood environments. The participants are individually experts drawn from a wide range of skills and disciplines being economists, mathematicians, psychologists, statisticians, physicists, software engineers and finance specialists. A number of the participants in this proposal have worked successfully together in the past and have produced leading research in this area but this project is the first to draw together the particular set of skills we feel we need to address the important issues we have identified. It is probably correct to state that this group includes some of the leading researchers in the area of agent based economics within Europe.