Thomas Lux

Scaling and criticality in a stochastic multi-agent model of a financial market

Financial prices have been found to exhibit some universal characteristics that resemble the scaling laws characterizing physical systems in which large numbers of units interact. This raises the question of whether scaling in finance emerges in a similar way — from the interactions of a large ensemble of market participants. However, such an explanation is in contradiction to the prevalent ‘efficient market hypothesis’ in economics, which assumes that the movements of financial prices are an immediate and unbiased reflection of incoming news about future earning prospects. Within this hypothesis, scaling in price changes would simply reflect similar scaling in the ‘input’ signals that influence them. Here we describe a multi-agent model of financial markets which supports the idea that scaling arises from mutual interactions of participants. Although the ‘news arrival process’ in our model lacks both power-law scaling and any temporal dependence in volatility, we find that it generates such behaviour as a result of interactions between agents.

THE SOCIO-ECONOMIC DYNAMICS OF SPECULATIVE MARKETS : INTERACTING AGENTS, CHAOS, AND THE FAT TAILS OF RETURN DISTRIBUTIONS

Abstract This paper develops a model of the social and economic interaction of speculators in a securities or foreign exchange market. Both chartist and fundamentalist strategies are pursued by traders. The formalization of chartists behavior combines elements of mimetic contagion and trend chasing leading to waves of optimism or pessimism. Furthermore, changes of strategies from chartist to fundamentalist behavior and vice versa occur because speculators compare the performance of both strategies. The dynamic system under study encompasses the time development of the distribution of attitudes among traders as well as price adjustment. Chaotic attractors are found within a broad range of parameter values. The distributions of returns derived from chaotic trajectories of the model share important characteristics of empirical data: they exhibit high peaks around the mean as well as fat tails (leptokurtosis) and become less leptokurtotic under time aggregation.

VOLATILITY CLUSTERING IN FINANCIAL MARKETS: A MICROSIMULATION OF INTERACTING AGENTS

The finding of clustered volatility and ARCH effects is ubiquitous in financial data. This paper presents a possible explanation of this phenomenon within a multi-agent framework of speculative activity. In the model, both chartist and fundamentalist strategies are considered with agents switching between both behavioural variants according to observed differences in pay-offs. Price changes are brought about by a market maker reacting on imbalances between demand and supply. Most of the time, a stable and efficient market results. However, its usual tranquil performance is interspersed by sudden transient phases of destabilisation. Outbreak of volatility occurs if the fraction of agents using chartist techniques surpasses a certain threshold value, but such phases are quickly brought to an end by stabilising tendencies. Formally, this pattern can be understood as an example of a new type of dynamic behaviour denoted on-off intermittency in physics literature. Statistical analysis of simulated data shows that the main stylised facts (unit roots in levels together with heteroscedasticity and leptokurtosis of returns) can be found in this artificial market.

The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks

A statistical analysis is provided of daily returns for 30 German stocks forming the DAX share index as well as the DAX itself during the period 1988–1994. Estimating the parameters of the stable laws and performing standard tests of fit, some evidence in favour of the stable Paretian hypothesis is found. However, application of a more recently developed semiparametric technique for analysis of the limiting behaviour in the tails of a distribution (Hills tail index estimator) suggests that the empirical tail regions are thinner than expected under a stable distribution. Since the reliability of tail index estimation rests on the appropriateness of the chosen tail regions, it is also examined whether the tails indeed follow approximately the expected limiting distributions of extremes. It turns out that convergence to the limiting extreme value distributions cannot be rejected in the vast majority of cases for tails covering the most extreme 15% of observations or less. Furthermore, strong similarity in t...

THE FINANCIAL CRISIS AND THE SYSTEMIC FAILURE OF THE ECONOMICS PROFESSION

ABSTRACT Economists not only failed to anticipate the financial crisis; they may have contributed to it—with risk and derivatives models that, through spurious precision and untested theoretical assumptions, encouraged policy makers and market participants to see more stability and risk sharing than was actually present. Moreover, once the crisis occurred, it was met with incomprehension by most economists because of models that, on the one hand, downplay the possibility that economic actors may exhibit highly interactive behavior; and, on the other, assume that any homogeneity will involve economic actors sharing the economist’s own putatively correct model of the economy, so that error can stem only from an exogenous shock. The financial crisis presents both an ethical and an intellectual challenge to economics, and an opportunity to reform its study by grounding it more solidly in reality.

The financial crisis and the systemic failure of academic economics

The economics profession appears to have been unaware of the long build-up to the current worldwide financial crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics. We trace the deeper roots of this failure to the professions focus on models that, by design, disregard key elements driving outcomes in real-world markets. The economics profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists undertake, as well as for the establishment of an ethical code that would ask economists to understand and communicate the limitations and potential misuses of their models.

Agent-based models of financial markets

This review deals with several microscopic (‘agent-based’) models of financial markets which have been studied by economists and physicists over the last decade: Kim–Markowitz, Levy–Levy–Solomon, Cont–Bouchaud, Solomon–Weisbuch, Lux–Marchesi, Donangelo– Sneppen and Solomon–Levy–Huang. After an overview of simulation approaches in financial economics, we first give a summary of the Donangelo–Sneppen model of monetary exchange and compare it with related models in economics literature. Our selective review then outlines the main ingredients of some influential early models of multi-agent dynamics in financial markets (Kim–Markowitz, Levy–Levy–Solomon). As will be seen, these contributions draw their inspiration from the complex appearance of investors’ interactions in real-life markets. Their main aim is to reproduce (and, thereby, provide possible explanations) for the spectacular bubbles and crashes seen in certain historical episodes, but they lack (like almost all the work before 1998 or so) a perspective in terms of the universal statistical features of financial time series. In fact, awareness of a set of such regularities (power-law tails of the distribution of returns, temporal scaling of volatility) only gradually appeared over the nineties. With the more precise description of the formerly relatively vague characteristics (e.g. moving from the notion of fat tails to the more concrete one of a power law with index around three), it became clear that financial market dynamics give rise to some kind of universal scaling law. Showing similarities with scaling laws for other systems with many interacting sub-units, an exploration of financial markets as multi-agent systems appeared to be a natural consequence. This topic has been pursued by quite a number of contributions appearing in both the physics and economics literature since the late nineties. From the wealth of different flavours of multi-agent models that have appeared up to now, we discuss the Cont–Bouchaud, Solomon–Levy–Huang and Lux–Marchesi models. Open research questions are discussed in our concluding section. 4 Now at Deutsche Bundesbank. The opinions expressed in this review are those of the authors, not those of the banks.

The Markov-Switching Multifractal Model of asset returns: GMM estimation and linear forecasting of volatility

Multifractal processes have recently been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns—a feature that has been found in virtually all financial data. Initial difficulties stemming from nonstationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multifractal model which allows for estimation of its parameters via maximum likelihood (ML) and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative generalized method of moments (GMM) estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular binomial and lognormal models and that the loss incurred with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series.

Testing for non-linear structure in an artificial financial market

We present a stochastic simulation model of a prototype financial market. Our market is populated by both noise traders and fundamentalist speculators. The dynamics covers switches in the prevailing mood among noise traders (optimistic or pessimistic) as well as switches of agents between the noise traders and fundamentalist group in response to observed differences in profits. The particular behavioral variant adopted by an agent also determines her decision to enter on the long or the short side of the market. Short-run imbalances between demand and supply lead to price adjustments by a market maker or auctioneer in the usual Walrasian manner. Our interest in this paper is in exploring the behavior of the model when testing for the presence of chaos or non-linearity in the simulated data. First, attempts to determine the fractal dimension of the underlying process give unsatisfactory results in that we experience a lack of convergence of the estimate. Explicit tests for non-linearity and dependence (the BDS and Kaplan tests) also give very unstable results in that both acceptance and strong rejection of IIDness can be found in different realizations of our model. All in all, this behavior is very similar to experience collected with empirical data and our results may point towards an explanation of why robustness of inference in this area is low. However, when testing for dependence in second moments and estimating GARCH models, the results appear much more robust and the chosen GARCH specification closely resembles the typical outcome of empirical studies.

Market Fluctuations I: Scaling, Multiscaling, and Their Possible Origins

In this chapter, we provide a survey of research on scaling phenomena in financial data pursued by physicists and compare their methodology and results with the approach of economists dealing with the same topic. We also try to put this work into perspective by discussing in how far it is reconcilable with traditional models in finance (the efficient market hypothesis) or whether it leads to a new viewpoint on market interactions.