Econophysics Review: I. Empirical Facts

Published as: Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca & Frédéric Abergel Econophysics Review 1: Empirical Facts Quantitative Finance, 11:7, 991-1012 (2011) http://dx.doi.org/10.1080/14697688.2010.539248 Econophysics Review: I. Empirical facts Anirban Chakrabortia) and Ioane Muni Tokeb) Laboratoire de Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, 92290 Châtenay-Malabry, France Marco Patriarcac) National Institute of Chemical Physics and Biophysics, Rävala 10, 15042 Tallinn, Estonia and Instituto de Fisica Interdisciplinaire y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain Frédéric Abergeld) Laboratoire de Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, 92290 Châtenay-Malabry, France (Dated: 3 November 2010) This article and its companion paper to follow aim at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words “Economics” and “Physics”, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modelling), econometrics of financial bubbles and crashes, etc. We discuss interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics. Then we present empirical studies reveal- ing statistical properties of financial time series. We begin the presentation with the widely acknowledged “stylized facts” which describe the returns of financial assets – fat tails, volatility clustering, autocorrelation, etc. – and recall that some of these properties are directly linked to the way “time” is taken into account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrating this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Finally, contributions to the study of correlations of assets such as random matrix theory and graph theory are presented. The following companion paper will review models in Econophysics through the point of view of agent-based modelling. Keywords: Econophysics; Stylized facts ; Financial time series; Correlations; Order book models ; Agent- based models; Wealth distributions; Game Theory; Minority Games; Pareto Law; Entropy maximization; Utility maximization. PACS Nos.: 05.45.Tp, 02.50.Sk, 05.40.-a, 05.45.Ra, 89.75.Fb I. INTRODUCTION And what little amount of information would be sufficient to infer some of their complex behaviours ? There exists a positive strive in answering these questions. In What is Econophysics? Fifteen years after the word the 1940’s, Majorana had taken scientific interest in fi- “Econophysics” was coined by H. E. Stanley by a merg- nancial and economic systems. He wrote a pioneering ing of the words ‘Economics’ and ‘Physics’, at an interna- paper on the essential analogy between statistical laws in tional conference on Statistical Physics held in Kolkata physics and in social sciences (di Ettore Majorana (1942); in 1995, this is still a commonly asked question. Many Mantegna (2005, 2006)). However, during the follow- still wonder how theories aimed at explaining the physical ing decades, only few physicists like Kadanoff (1971) or world in terms of particles could be applied to understand Montroll and Badger (1974) had an explicit interest for complex structures, such as those found in the social and research in social or economic systems. It was not until economic behaviour of human beings. In fact, physics as the 1990’s that physicists started turning to this interdis- a natural science is supposed to be precise or specific; its ciplinary subject, and in the past years, they have made predictive powers based on the use of a few but universal many successful attempts to approach problems in vari- properties of matter which are sufficient to explain many ous fields of social sciences (e.g. de Oliveira et al. (1999); physical phenomena. But in social sciences, are there Stauffer et al. (2006); Chakrabarti et al. (2006)). In par- analogous precise universal properties known for human ticular, in Quantitative Economics and Finance, physics beings, who, on the contrary of fundamental particles, research has begun to be complementary to the most tra- are certainly not identical to each other in any respect ? ditional approaches such as mathematical (stochastic) finance. These various investigations, based on methods imported from or also used in physics, are the subject of the present paper. a)Electronic mail: [email protected] b)Electronic mail: [email protected] c)Electronic mail: marco.patriarca@kbfi.ee d)Electronic mail: [email protected] 2 A. Bridging Physics and Economics include examples from physics, chemistry, biology and also social sciences. The concepts and methods of sta- Economics deals with how societies efficiently use their tistical physics turned out to be extremely useful in ap- resources to produce valuable commodities and distribute plication to these diverse complex systems including eco- them among different people or economic agents (Samuel- nomic systems. Many complex systems in natural and son (1998); Keynes (1973)). It is a discipline related to social environments share the characteristics of compe- almost everything around us, starting from the market- tition among interacting agents for resources and their place through the environment to the fate of nations. At adaptation to dynamically changing environment (Parisi first sight this may seem a very different situation from (1999); Arthur (1999)). Hence, the concept of disordered that of physics, whose birth as a well defined scientific systems helps for instance to go beyond the concept of theory is usually associated with the study of particular representative agent, an approach prevailing in much of mechanical objects moving with negligible friction, such (macro)economics and criticized by many economists (see as falling bodies and planets. However, a deeper compar- e.g. Kirman (1992); Gallegati and Kirman (1999)). Mi- ison shows many more analogies than differences. On a nority games and their physical formulations have been general level, both economics and physics deal with “ev- exemplary. erything around us”, despite with different perspectives. Physics models have also helped bringing new theories On a practical level, the goals of both disciplines can be explaining older observations in Economics. The Italian either purely theoretical in nature or strongly oriented social economist Pareto investigated a century ago the toward the improvement of the quality of life. On a more wealth of individuals in a stable economy (Pareto (1897)) technical side, analogies often become equivalences. Let by modelling them with the distribution P (> x) x−α, us give here some examples. where P (> x) is the number of people having ∼income Statistical mechanics has been defined as the greater than or equal to x and α is an exponent (known now as the Pareto exponent) which he estimated to be “branch of physics that combines the prin- 1.5. To explain such empirical findings, physicists have ciples and procedures of statistics with the come up with some very elegant and intriguing kinetic laws of both classical and quantum mechan- exchange models in recent times, and we will review ics, particularly with respect to the field of these developments in the companion article. Though thermodynamics. It aims to predict and ex- the economic activities of the agents are driven by various plain the measurable properties of macro- considerations like “utility maximization”, the eventual scopic systems on the basis of the properties exchanges of money in any trade can be simply viewed and behaviour of the microscopic constituents as money/wealth conserving two-body scatterings, as in 1 of those systems.” the entropy maximization based kinetic theory of gases. This qualitative analogy seems to be quite old and both The tools of statistical mechanics or statistical physics economists and natural scientists have already noted (Reif (1985); Pathria (1996); Landau (1965)), that in- it in various contexts (Saha et al. (1950)). Recently, clude extracting the average properties of a macroscopic an equivalence between the two maximization principles system from the microscopic dynamics of the systems, are have been quantitatively established (Chakrabarti and believed to prove useful for an economic system. Indeed, Chakrabarti (2010)). even though it is difficult or almost impossible to write down the “microscopic equations of motion” for an eco- Let us discuss another example of the similarities of in- nomic system with all the interacting entities, economic terests and tools in Physics and Economics. The friction- systems may be investigated at various size scales. There- less systems which mark the early history of physics were fore, the understanding of the global behaviour of eco- soon recognized to be rare cases: not only at microscopic nomic systems seems to need concepts such as stochas- scale – where they obviously represent an exception due tic dynamics, correlation effects, self-organization, self- to the unavoidable interactions with the environment – similarity and scaling, and for their application we do but also at the macroscopic scale, where fluctuations of not have to go into the detailed “microscopic” descrip- internal or external origin make a prediction of their tion of the economic system. time evolution

Load more