Econophysics is an interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics.

History[link]

Physicists’ interest in the social sciences is not new; Daniel Bernoulli, as an example, was the originator of utility-based preferences. One of the founders of neoclassical economic theory, former Yale University Professor of Economics Irving Fisher, was originally trained under the renowned Yale physicist, Josiah Willard Gibbs.^[1] Likewise, Jan Tinbergen, who won the first Nobel Prize in economics in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with Paul Ehrenfest at Leiden University.

Econophysics was started in the mid-1990s by several physicists working in the subfield of statistical mechanics. Unsatisfied with the traditional explanations and approaches of economists - which usually prioritized simplified approaches for the sake of soluble theoretical models over agreement with empirical data - they applied tools and methods from physics, first to try to match financial data sets, and then to explain more general economic phenomena.

One driving force behind econophysics arising at this time was the sudden availability of large amounts of financial data, starting in the 1980s. It became apparent that traditional methods of analysis were insufficient - standard economic methods dealt with homogeneous agents and equilibrium, while many of the more interesting phenomena in financial markets fundamentally depended on heterogeneous agents and far-from-equilibrium situations.

The term “econophysics” was coined by H. Eugene Stanley in the mid 1990s, to describe the large number of papers written by physicists in the problems of (stock and other) markets, and first appeared in a conference on statistical physics in Calcutta in 1995 and its following publications. The inaugural meeting on Econophysics was organised 1998 in Budapest by János Kertész and Imre Kondor.

Currently, the almost regular meeting series on the topic include: Econophysics Colloquium, ESHIA/ WEHIA, ECONOPHYS-KOLKATA, APFA

In the last years, networks science, heavily reliant on analogies from Statistical mechanics, has been applied to the study of productive systems. That is the case with the works done at the Santa Fe Institute and the Harvard-MIT Observatory of Economic Complexity

If "econophysics" is taken to denote the principle of applying statistical mechanics to economic analysis, as opposed to a particular literature or network, priority of innovation is probably due to Farjoun and Machover (1983). Their book Laws of Chaos: A Probabilistic Approach to Political Economy proposes dissolving (their words) the transformation problem in Marx's political economy by re-conceptualising the relevant quantities as random variables.

If, on the other side, "econophysics" is taken to denote the application of physics to economics, one can already consider the works of Léon Walras and Vilfredo Pareto as part of it. Indeed, as shown by Ingrao and Israel, general equilibrium theory in economics is based on the physical concept of mechanical equilibrium.

Econophysics has nothing to do with the "physical quantities approach" to economics, advocated by Ian Steedman and others associated with Neo-Ricardianism. Notable econophysicists are Jean-Philippe Bouchaud, Bikas K Chakrabarti, Dirk Helbing, Tobias Preis, János Kertész, Matteo Marsili, Joseph L. McCauley, Enrico Scalas, Didier Sornette, H. Eugene Stanley, Victor Yakovenko and Yi-Cheng Zhang. Particularly noteworthy among the formal courses on Econophysics is the one offered by the Physics Department of the Leiden University,^[2] from where the first Nobel-laureate in economics Jan Tinbergen came.

Basic tools[link]

Basic tools of econophysics are probabilistic and statistical methods often taken from statistical physics.

Physics models that have been applied in economics include percolation models, chaotic models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for earthquake prediction.^[3] Moreover, there have been attempts to use the mathematical theory of complexity and information theory, as developed by many scientists among whom are Murray Gell-Mann and Claude E. Shannon, respectively.

Since economic phenomena are the result of the interaction among many heterogeneous agents, there is an analogy with statistical mechanics, where many particles interact; but it must be taken into account that the properties of human beings and particles significantly differ.

Another good example is random matrix theory, which can be used to identify the noise in financial correlation matrices. It has been shown that this technique can significantly improve the performance of portfolios, e.g., in applied in portfolio optimization.^[4] Thus, this practice is commonly encountered in the praxis of quantitative finance.

There are, however, various other tools from physics that have so far been used with mixed success, such as fluid dynamics, classical mechanics and quantum mechanics (including so-called classical economy, quantum economy and quantum finance), and the path integral formulation of statistical mechanics.

The concept of economic complexity index, introduced by the Harvard economist Ricardo Hausmann and the MIT physicist Cesar Hidalgo, has been further developed at the Harvard-MIT Observatory of Economic Complexity, has been devised as a predictive tool for economic growth. According to the estimates of Hausmann and Hidalgo, the ECI is far more accurate in predicting GDP growth than the traditional governance measures of the World Bank.^[5]

There are also analogies between finance theory and diffusion theory. For instance, the Black-Scholes equation for option pricing is a diffusion-advection equation (see however ^[6][7] for a critique of the Black-Scholes methodology).

Impact on mainstream economics and finance[link]

Papers on econophysics have been published primarily in journals devoted to physics and statistical mechanics, rather than in leading economics journals. Mainstream economists have generally been unimpressed by this work.^[8] Some Heterodox economists, including Mauro Gallegati, Steve Keen and Paul Ormerod, have shown more interest, but also criticized trends in econophysics.

In contrast, econophysics is having some impact on the more applied field of quantitative finance, whose scope and aims significantly differ from those of economic theory. Various econophysicists have introduced models for price fluctuations in financial markets or original points of view on established models.^[6][9] Also several scaling laws have been found in various economic data.^[10][11][12]

Main results[link]

Presently, the main results of econophysics comprise the explanation of the "fat tails" in the distribution of many kinds of financial data as a universal self-similar scaling property (i.e. scale invariant over many orders of magnitude in the data),^[13] arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the risks, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not neglegible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a failure probability of only Failed to parse (Missing texvc executable; please see math/README to configure.): P\propto x^{-4}\,,

where x is an increasingly large variable  in the tail region of the distribution considered (i.e. a price statistics with much more than 108 data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away". [14]  It appears that it also plays a role that near a change of the tendency (e.g. from falling to rising prices) there are typical "panic reactions" of the selling or buying agents with algebraically increasing bargain rapidities and  volumes. [14] 
 

As in quantum field theory the "fat tails" can only be obtained by complicated "nonperturbative" methods, mainly by numerical ones, since they contain the deviations from the usual Gaussian approximations, e.g. the Black-Scholes theory.

See also[link]

Physics portal

• Bose–Einstein condensation (network theory)
• Complexity economics
• Complex network
• Detrended fluctuation analysis
• Kinetic exchange models of markets
• Long-range dependency
• Network theory
• Network science
• Thermoeconomics

References[link]

Further reading[link]

Textbooks[link]

• Rosario N. Mantegna, H. Eugene Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press (Cambridge, UK, 1999)
• Vladimir N Pokrovskii, Econodynamics. The Theory of Social Production, Springer: Berlin (2011).
• Nicholas Georgescu-Roegen, The Entropy Law and the Economic Process, Harvard University Press: Cambridge, Massachusetts, 1971.
• Johannes Voit, The Statistical Mechanics of Financial Markets, Springer; 3rd edition (Berlin 2005)
• Sitabhra Sinha, Arnab Chatterjee, Anirban Chakraborti, Bikas K Chakrabarti. Econophysics: An Introduction, Wiley-VCH (2010)
• Jean-Philippe Bouchaud, Marc Potters, Theory of Financial Risk and Derivative Pricing, Cambridge University Press (Cambridge, UK, 2003)
• Bikas K Chakrabarti, Anirban Chakraborti, Arnab Chatterjee, Econophysics and Sociophysics : Trends and Perspectives, Wiley-VCH, Berlin (2006)
• Joseph McCauley, Dynamics of Markets, Econophysics and Finance, Cambridge University Press (Cambridge, UK, 2004)
• Bertrand Roehner, Patterns of Speculation - A Study in Observational Econophysics, Cambridge University Press (Cambridge, UK, 2002)
• Arnab Chatterjee, Sudhakar Yarlagadda, Bikas K Chakrabarti, Econophysics of Wealth Distributions, Springer-Verlag Italia (Milan, 2005)
• Keith Meyer, Extending and simulating the quantum binomial options pricing model, University of Manitoba (Winnipeg, 2009)
• Hagen Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd edition, World Scientific (Singapore, 2004) also available online on physik.fu-berlin.de
• Emmanuel Farjoun and Moshe Machover, Laws of Chaos; A Probabilistic Approach to Political Economy, London: Verso, 1983. Probabilisticpoliticaleconomy.net
• Philip Mirowski, More Heat than Light - Economics as Social Physics, Physics as Nature's Economics, Cambridge University Press (Cambridge, UK, 1989)
• Bruna Ingrao and Giorgio Israel, The Invisible Hand - Economic Equilibrium in the History of Science, The MIT Press (Cambridge, MA, 1990).
• Didier Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems, Princeton University Press (2004).
• Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Mathematical modelling of collective behavior in socio-economic and life sciences, Birkhauser, (2010).
• Reiner Kümmel, The Second Law of Economics: Energy, Entropy, and the Origins of Wealth, Springer: Berlin (2011).
• Ubaldo Garibaldi and Enrico Scalas, Finitary Probabilistic Methods in Econophysics, Cambridge University Press (Cambridge, UK, 2010).

Journal articles[link]

• Mauro Gallegati, Steve Keen, Thomas Lux and Paul Ormerod, Worrying Trends in Econophysics, Physica A 370, 1-6 (2006).
• Special issue of the Journal of Economic Dynamics and Control, January 2008: 'Applications of statistical physics in economics and finance'.
• Mantegna, Rosario N.; Kertesz, Janos (2010). "Focus on Statistical Physics Modelling in Economics and Finance". New Journal of Physics. http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Statistical%20Physics%20Modelling%20in%20Economics%20and%20Finance. 
• V. M. Yakovenko and J. B. Rosser, Jr. "Colloquium: Statistical mechanics of money, wealth, and income", Reviews of Modern Physics 81, 1703 (2009)
• Special issue of 'SCIENCE AND CULTURE', September–October 2010, Volume 76, N.9-10 'On 15 Years of Econophysics Research'.
• Tobias Preis; H. Eugene Stanley (2011). "Bubble trouble: Can a Law Describe Bubbles and Crashes in Financial Markets?". Physics World 24 (5): 29–32. http://tobiaspreis.de/publications/ps_pw_2011.pdf. 
• Tobias Preis, T.; Johannes J. Schneider; H. Eugene Stanley (2011). "Switching processes in financial markets". Proceedings of the National Academy of Sciences 108 (19): 7674–7678. Bibcode 2011PNAS..108.7674P. DOI:10.1073/pnas.1019484108. http://www.pnas.org/cgi/doi/10.1073/pnas.1019484108. 

Lectures[link]

• Economic Fluctuations and Statistical Physics: Quantifying Extremely Rare and Much Less Rare Events, Eugene Stanley, Videolectures.net
• Applications of Statistical Physics to Understanding Complex Systems, Eugene Stanley, Videolectures.net
• Financial Bubbles, Real Estate Bubbles, Derivative Bubbles, and the Financial and Economic Crisis, Didier Sornette, Videolectures.net
• Financial crises and risk management, Didier Sornette, Videolectures.net
• Bubble trouble: how physics can quantify stock-market crashes, Tobias Preis, Physics World Online Lecture Series

External links[link]

• Econophysics Ph.D. Program at University of Houston, Houston, TX.
• Yuri Yegorov, article Econo-physics: A Perspective of Matching Two Sciences, Evol. Inst. Econ. Rev. 4(1): 143–170 (2007)
• Finance Gets Physical - Yale Economic Review
• Econophysics Forum
• Introduzione alla Econofisica in logica complementare
• Anatoly Kondratenko. Physical Modeling of Economic Systems. Classical and Quantum Economies
• Econophysics Research in Victor Yakovenko's group
• Econophysics Research in Thomas Guhr's group
• Evolutionary and Institutional Economics Review (Freely downloadable)

Tobias Preis (* July 23, 1981) is a German complex systems scientist focussing on analysis and prediction of social and financial complexity captured in big data. He is a Senior Research Fellow at Boston University and a Visiting Lecturer at University College London. In 2007, he founded Artemis Capital Asset Management GmbH, a proprietary trading firm which is based in Germany. In 2009, he was named a member of the Gutenberg Academy. He was awarded a Ph.D. in physics from the Johannes Gutenberg University of Mainz in Germany.

Preis has quantified and modelled financial market fluctuations^[1][2]. In addition, he has made contributions to general-purpose computing on graphics processing units (GPGPU) in statistical physics^[3][4] and computational finance.^[5]

In 2010, Preis headed a research team which provided evidence that search engine query data and stock market fluctuations are correlated.^{[6][7][8][9][10]} The team discovered a link between the number of Internet searches for company names and and transaction volumes of the corresponding stocks on a weekly time scale. In a TEDx talk^[11], Preis highlights the opportunities offered by studies of citizens' online behaviour to gain insights into socio and economic decision making.

In 2012, Preis used Google Trends data to demonstrate together with his colleagues Helen Susannah Moat, H. Eugene Stanley and Steven R. Bishop that Internet users from countries with a higher per capita gross domestic product (GDP) are more likely to search for information about the future than information about the past. The findings, published in the journal Scientific Reports, suggest there may be a link between online behaviour and real-world economic indicators.^{[12][13][14][15]} Preis and colleagues examined Google search queries made by Internet users in 45 different countries in 2010 and calculated the ratio of the volume of searches for the coming year (‘2011’) to the volume of searches for the previous year (‘2009’), which they call the ‘future orientation index’. A comparison of the future orientation index to the per capita GDP of each country revealed a strong tendency for countries in which Google users enquire more about the future to exhibit a higher GDP. Preis and colleagues conclude from this study that a relationship potentially exists between the economic success of a country and the information-seeking behaviour of its citizens online.^[12]

Footnotes[link]

External links[link]

• "CV of Tobias Preis". http://www.tobiaspreis.de/cv.html. Retrieved February 2, 2011. 
• "TEDx talk by Tobias Preis - Bubble Trouble". http://www.youtube.com/watch?v=fJWi_6s10nw. Retrieved October 22, 2011.