Econophysics

The econophysics ( English : Econophysics ) is an interdisciplinary field that deals with the application of methods and theories, originally of physics , busy originate on economic issues. In this context, mainly non-linear dynamics and tools from statistical mechanics are used. Especially in the area of financial markets , this approach led to new insights and the discovery of so-called robust power laws (that is, in the jargon of physics: "scale behavior with universal fractal exponents").

Economic physics is about the description of complex , dynamic systems using mathematical models . In econophysics, in addition to ex-post modeling - especially in the area of ​​stock market collapses ("crashes") in a group led by the French physicist Didier Sornette - ex-ante forecasts are formulated and checked, whereby the "bubbles" and " Crashes ”of the financial markets can be interpreted as“ singular phenomena ”in the sense of physics. Economic physics tries to prove robust relationships even in larger systems with several variables, for example in the area of portfolios . In doing so, the physicist concentrates only on the so-called “ relevant ” phenomena that have been precisely treated .

History and rationale

The beginning of the 1990s is seen as the beginning of econophysics. The flood of economic data from the 1980s and dissatisfaction with traditional explanations encouraged physicists to use insights from statistical mechanics to explore economics. The term econophysics goes back to the physicist Eugene Stanley , who first introduced the term.

The actual initial spark for this new science can be found in the mid-1980s, when the Santa Fe Institute was founded. Mainly directed by physicists and economists , the institute's economic program included the first attempts towards a fundamentally changed economic science. This perceived markets and the national economy as the result of an interaction of many heterogeneous agents in which the phenomenon of so-called emergence plays a decisive role. It was in contrast to the neoclassical traditional economics , which is based on homogeneous market participants (see also the molecular field approximation in physics) and takes a micro-based view.

Other pioneers of econophysics were z. B. the CCISF of the University of Nice (especially self-organized criticality), the University of Boston (especially turbulence physics) and the University of Cologne (especially phase transition).

Impact on Traditional Economics

In the course of history, the development of economics has repeatedly been characterized by the adoption of scientific knowledge, particularly from physics. Influenced by the work of Isaac Newton , the philosopher Auguste Comte developed a vision of social physics in the first half of the 19th century . Alfred Marshall's and Francis Edgeworth's subsequent equilibrium theories were based on the work of James Clerk Maxwell and Ludwig Boltzmann on the statistical behavior of individual agents. This form of interdisciplinary cooperation or the adoption of concepts came to a virtual standstill in the 1930s and only experienced a renaissance in the 1980s.

During this period, the prevalent economic theories were the assumption of Homo oeconomicus , the (to put it simply) rationally acting utility maximizer, interdisciplinary research on complex adaptive systems was carried out in the natural sciences . The idea of ​​rationally acting actors in a real system, such as the national economy, is rejected as being oversimplified. Instead, a stable behavior as a whole develops (“emerges”) from the seemingly chaotic interplay of the behavior of the individually acting agents. The macro-economy therefore develops from the micro-economy. This is in contrast to the traditionally rather strong separation of these two levels, in which the border crossing is understood as "fundamental" and consequently applied too early (which in physicists' jargon creates an approximation from the outset, precisely the molecular field approximation). While the market in classical economics develops an equilibrium in which the markets are "cleared" and market price distributions follow a Gaussian normal distribution (at best a Gaussian distribution that is " optimized " in some sense ), complex systems are subject to constant fluctuations until the end and are not sufficient- Gaussian distributions, such as a. Benoît Mandelbrot showed in his study of stock exchange prices in 1963.

Analogies to the turbulence theory u. Ä.

In physically motivated theories, the similarities to turbulence theory , to weather events ( meteorology ) and to earthquake research ( seismology ) are repeatedly pointed out. The similarity concerns on the one hand the point of view that one is dealing with random processes in these theories, so that one basically does not have to work with ordinary or partial differential equations, but with so-called stochastic differential equations or renormalization theories . The other point of view concerns the self-similarity of the processes; H. Among other things, the scale behavior over many powers of ten: In turbulence physics one has z. B. "small eddies within larger eddies", and within the small eddies again and again smaller, a whole hierarchy of self-similar eddies on all scales. This self-similarity corresponds to what one observes in correlation analyzes of stock exchange prices over many time scales.

In turbulence physics, the "self-similarity" with regard to the vortex spectrum has been able to be converted into a complete scale theory of the energy scales of a turbulent flow after many decades (see Andrei Kolmogorow and Turbulent Flow # Energy Cascade ). Unfortunately, something similar is missing in the other areas, so that so far one has to restrict oneself to numerical investigations.

Basic concepts

Econophysics is a further development of a dynamic economic understanding in economics. Findings such as the Neo-Schumpeterian growth model and the endogenous growth theory , which point to an evolution-like course of economic development history, corroborated a view "... that the stable equilibrium is more of an exception than the norm. (... that stable equilibrium is more the exception than is the rule.) "  With this view originally physical concepts such as B. Chaos , so-called power laws , self-organized criticality and the associated notion of evolutionary economics in the foreground of the investigations. The approach and modeling of econophysics is similar to that of complex physical phenomena. Your research has a clear focus on the financial markets. Further areas are the distribution of income and wealth, the distribution of economic shocks and growth rates, company sizes and growth rates, the development of urban societies and much more

Power Law Distribution (PLD)

At the end of the 19th century Pareto provided the first approaches to an “econophysical” description of economic activity with the discovery that the distribution of wealth in a society can be described with a statistical probability distribution of the form , with the number of people who have an income and the characteristic Exponent, whose value Pareto estimated at 1.5. Pareto showed that this power law (statistics) could be applied approximately for nations as different as England, Ireland or Germany, but also for Italian cities or Peru. In the context of modern econophysics, such PLDs were z. B. for the distribution of the trading volume on different stock exchanges, the size distribution of certain investment funds, as well as for the dependence of the transaction volume on the volatility of the prices for certain securities. With increasing detailing of the postulated power law distribution ( PLD), however, doubts about the underlying universality of the PLDs and criticism of the admissibility of the methods used are expressed, so that further research in this area remains to be seen. ${\displaystyle y\thicksim x^{-\alpha }}$ ${\displaystyle y}$ ${\displaystyle \geq x}$ ${\displaystyle \alpha }$

Instead of the so-called random walks (“odyssey”) of statistical physics, which lead to Gaussian distributions, the more general so-called Lévy flights are to be listed.

Covariance

A twin property to the quasi-universality of the PLD is the hyperbolic decline in the covariance of any units of measure of volatility (e.g., price fluctuations). The simplest and most well-known unit of measurement for volatility is based on the least squares method , in which volatility is given as the square root of the sum of all squares of fluctuations in a time series, whereby the direction of the fluctuations is not taken into account. When looking at the strength of the correlation over time, for example through , corresponding empirical studies suggest that the greater the fluctuations in the past, the greater the expected fluctuations in future market prices (volatility clustering). ${\displaystyle \mathrm {Cov\,} \,\langle |r_{t}|;|r_{t-\delta t}|\rangle \thicksim \delta t^{-\gamma }}$

Multi-fractal models

In a further development of the ARCH and GARCH models known in economics , so-called multi-fractal models were introduced into the study. In the mathematical modeling of financial data, in particular, these map the so-called multi-scaling properties, whereby they refer to models of turbulence physics. Further models were then integrated into these approaches, such as Brownian molecular motion or so-called Markov switching multifractal models.

Study areas

Financial markets

Exchange structure

Empirical research has provided valuable insights into the structural analysis of stock exchanges. The distribution of incoming new orders with a limit price follows a power law as long as the incoming orders are close to the respective market price. Studies for different stock exchanges have shown, however, that the coefficient of the power law can differ greatly (e.g. 0.6 for Paris and 1.5 for London). Others have observed the power law for the dependence of the transaction volume on the volatility of the corresponding prices.

Stock market price volatility

Share prices usually show a volatile behavior, which can be seen in analogy to dynamic turbulence in liquids, for example. This has led to an attempt to apply the physical approaches of fluid mechanics to economic processes in the context of econophysics.

Another interesting approach in econophysics in forecasting stock market crashes comes from earthquake research and the knowledge that certain, periodically oscillating preliminary activities can be determined before major earthquakes. Economists applied this approach to the stock market crash of August 1997 and postulated that stock market prices follow a logarithmic periodicity pattern that can be described by a dynamic earthquake equation (see also: Intermittenz ). However, the approach is quite controversial in the literature

Wealth distribution

Another research area in econophysics is the study of the nature of imbalances in the distribution of income and wealth in an economic system. The PLD for high incomes identified by Pareto in 1897 could subsequently be verified empirically for many systems as mentioned above. Recent research in this area indicates that within the underlying distribution functions, "phase transitions" of different distribution functions can also occur.

Another pioneering approach in econophysics to this topic comes from the sociologist John Angle and combines approaches from particle physics with anthropology. Further developments of this approach show u. a. the system behavior with constant money supply, with random determination of the loss of prosperity or with simultaneous interaction between all members of the population.

Industrial size

One of the areas with the best statistical data series is the cross-sector recording of company parameters such as turnover, number of employees, etc. over time. One of the most extensive analyzes of this company data comes from the Boston Group and relates to companies that are represented in the S&P COMPUSTAT Index. The findings of this series of studies indicate that the size distribution of US companies follows a log-normal distribution and that there is a linear relationship between the logarithm of the standard deviation of the growth rate of companies and the logarithm of company size.

Other areas

Other areas of econophysics concern the structural development of urban areas and the investigation of innovation as a motor of economic development.

Opposing viewpoints (criticism)

Important input in the type of underlying models from physics comes from the areas of statistical physics, fluid mechanics, earthquake prediction and self-organized criticality. In particular, the slowly falling tail areas (the so-called "fat tails") in the distributions of price changes of securities were discovered as an important universal property of financial markets. Furthermore, within the framework of the new discipline, findings and assumptions of economics could be corroborated (e.g. the right-skewed distribution of company sizes or the decrease in the spread of company growth with increasing size). As in quantum field theory, the "fat tails" can only be obtained using diagrammatic methods or computer simulations, because they result in deviations from Gauss law . However, it is precisely these terms that contain the essentials, namely the often very small, but nonetheless not to be neglected “ risk distributions ”. It turns out that the big risks can never be made exponentially small, but only follow a decreasing power law, something like where a variable in the tail area of ​​the distribution under consideration means that quantifies the “bet” made. It seems that the self-similarity comes about through the tendency of the individual market participants to systematically optimally exploit the respective positive or negative market trend (rising or falling prices), and that when the respective trend changes, real "panic reactions" with enormously shortened trading intervals and enormously increasing trading volumes occur. ${\displaystyle R\propto x^{-4}\,,}$ ${\displaystyle x\,\,(\to \infty )}$

Nevertheless, criticism of the discipline of econophysics is loud in the literature. As part of the World Econophysics Colloquium 2005, a working paper was presented that summarizes the so-called Worrying Trends in Econophysics , in particular:

• Lack of knowledge of the knowledge gained and the processes used in the course of economic research
• Resistance to solid protection of statistical procedures
• Believe in universal properties for all areas of economic activity
• Use of incorrect, oversimplified, or incomplete theoretical models

In addition, the econophysicists are repeatedly accused of not contributing to the specific questions of risk assessment.

The authors of the Worrying Trends cite numerous examples in which the assumed probability distributions have turned out to be incorrect upon closer statistical examination, and suggest that the hypotheses that have been established should be statistically validated more strictly than before in empirical studies. Furthermore, reference is made to the fact that production and not exchange is the engine of economic growth and therefore the frequent use of exchange models for the analysis of growth processes is useless. The further discussion remains to be seen.

Criticism of the approach of the economics physicists also refers to an extensive ignorance of the "idea, history and cultural background of the problem" as well as the literature, and the restriction to pure data analysis and thus the financial markets in which the best data situation is available. The field to be examined, however, includes a much larger spectrum in which the financial markets only play a small role. As a result, a large part of econophysical articles are published in explicitly physical science magazines by physicists, or in magazines specially created for econophysics such as the Journal of Economic Interaction and Coordination .
An example in this context is an Ising model , which physicists describe with a so-called Hamilton    function, where the binary variables are and the quantities mean quantities and real numbers. The indices and run through a basic set called a "graph". The whole thing becomes an economic model if it is interpreted as follows: "Agent" i makes a positive or negative purchase decision at time t under the influence of the then prevailing "economic situation" - this is analogous to the physicists' concept of temperature - based on the current price , the current so-called "news" , i.e. due to the current trend, and due to the so-called "herd effect". Instead, the physicist speaks of the basic energy, the so-called external bias field ("Zeeman field") and the so-called. "Exchange interaction" (e.g. with the respective neighbors ). ${\displaystyle {\mathcal {H}}=E_{0}(t)-\sum _{i,k}\,J_{i,k}\,s_{i}\,s_{k}-\sum _{i}H_{i}(t)\,s_{i}}$ ${\displaystyle s_{i}}$ ${\displaystyle (\,=\pm 1\,)}$ ${\displaystyle E_{0}(t),\,\,J_{i,k}}$ ${\displaystyle H_{i}(t)}$ ${\displaystyle i}$ ${\displaystyle k}$ ${\displaystyle (s_{i}=+1)}$ ${\displaystyle (s_{i}=-1)}$ ${\displaystyle E_{0}(t)}$ ${\displaystyle H_{i}(t)}$ ${\displaystyle J_{i,k}\,.}$ ${\displaystyle k}$

From the economists' point of view, this model would be far too simplistic and therefore “unrealistic”. The physicist, on the other hand, says that he only cares about very specific relevant relationships and that deviations in detail could be irrelevant, especially when it comes to scale problems. From the point of view of the physicists, the apparently far too simplified approach still contains exactly the essentials, which can only be seen if, as in the formulas of the economic physicists, the collective effects are rigorously (i.e. approximate!) Considered, which is the case. (With the specified model - and many other models - this is possible.) In contrast, the exact time of a "catastrophe" (e.g. an earthquake) cannot be predicted at all because it depends on imponderables (e.g. on unknown material properties such as the breaking strength or the buckling load ). But you can give the approximate strength of the "quake" and quantitative indications of when certain hazards occur, where the risks are and how great they are, and what effects are to be expected.

See also

• Sociophysics
• Critical phenomenon

literature

• Hagen Kleinert : Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets . World Scientific Publishing, 2006, ISBN 981-270-009-9 .
• Rosario N. Mantegna , H. Eugene Stanley : An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge 1999, ISBN 0-521-62008-2 .
• Sitabhra Sinha, Arnab Chatterjee, Anirban Chakraborti, Bikas K Chakrabarti: Econophysics: An Introduction. Wiley-VCH, 2010.
• H. Eugene Stanley, Tobias Preis: Bubble trouble: Can a Law Describe Bubbles and Crashes in Financial Markets? In: Physics World . tape 24 , no. 5 , 2011, p. 29–32 ( online [PDF]).
• Didier Sornette: Why Stock Markets Crash: Critical Events in Complex Financial Systems . Princeton University Press, Princeton 2003.
• Johannes Voit: The Statistical Mechanics of Financial Markets . Springer, Berlin / Heidelberg / New York 2000, ISBN 3-540-26285-7 .
• M. Mitchell Waldrop: Complexity: The Emerging Science at the Edge of Order and Chaos . Simon & Schuster, New York 1992, ISBN 0-671-87234-6 .
• Z. Slanina: Essentials of Econophysics modeling. Oxford University Press 2014, ISBN 978-0-19-929968-3 . (very extensive)
• P. Richmond, J. Mimkes, S. Hitzler: Econophysics & Physical Economy. Oxford Univ. P. 2013, ISBN 978-0-19-967470-1 . (shorter)

Video lectures

There are many lectures and lectures on the topic of the article which, in contrast to the following two "video lectures" , are usually not reproducible:

• Applications of Statistical Physics to Understanding Complex Systems , complete video of a lecture (approx. 1 hour, topic "Economics" from min. 24) at an international conference on economic physics in September 2008, just after the collapse of the Lehman Brothers bank , (on-line)
• Financial crises and risk management , Didier Sornette , (online) (very general, Ljubljana -Conf. "Risc '08", approx. 3/2 hours, including the very long "discussion" after the lecture)

Web links

• Chair for money, currency and international financial markets at the Christian-Albrechts-Universität zu Kiel
• Chair for Economics, especially International Economics at the Otto-Friedrich-Universität Bamberg
• Complex Systems Lab of the Institute for Theoretical Physics at the University of Bremen
• Article on the subject of econophysics. ( Memento from February 11, 2013 in the web archive archive.today ) In: Financial Times Deutschland , May 8, 2003
• Article on the subject of econophysics. In: NZZ , May 18, 2011
• Homepage of the Santa Fe Institute (English)
• Econophysics Forum of the University of Friborg (English)

Individual evidence

1. ↑ Mantegna and Stanley give a supplementary definition : They call Ökonophysik “… [as] a neologism that denotes the activities of physicists that are working on economic problems to test a variety of new conceptual approaches deriving from the physical sciences”. (Mantegna, Stanley, 1999, pp. Xiii-ix) They also characterize the discipline of econophysics according to who is working on them.
2. ^ Duncan K. Foley: Statistical Equilibrium in Economics: Method, Interpretation, and an Example . In: XII Workshop on “General Equilibrium: Problems, Prospects and Alternatives” . 1999, p. 25 ( Citeseer ).
3. ↑ "Robust" means here: "insensitive to insignificant disturbances", i. H. while maintaining the "essential" properties. The task remains to determine which properties are “essential” or “relevant” in this sense and which are not .
4. ↑ See e.g. B. See Didier Sornette, A. Johansen, JP Bouchaud: Stock market crashes, precursors and replicas. In: Journal de Physique I 6 (1). 1996, pp. 167-175 or Didier Sornette, Johansen: Large Financial Crashes. In: Physica A 245, 1997, pp. 411-422.
5. ↑ Cf. Didier Sornette, W.-X. Zhou: The US 2000-2002 market descent: How much longer and deeper? In: Quantitative Finance 2. 2002, or: XW Zhou, D. Sornette: Evidence of a worldwide stockmarket log-periodic anti-bubble since mid-2000. In: . Physica A 330. 2003.
6. ^ Thomas Lux: Applications of Statistical Physics in Finance and Economics . (PDF) In: Economic Working Papers 05-2007 CAU , Kiel.
7. ↑ Tobias Prize: Ökonophysik p. 2, 2011
8. ^ Center for Complexity and Interdisciplinary Studies in Finance. from the University of Nice Sophia Antipolis.
9. ↑ See also Dietrich Stauffer
10. ↑ A. Carbone, G. Kaniadakis, AM Scarfone: Where do we stand on Econophysics? In: Physica A. 08.2007, Volume 382, ​​Issue 1, pp. Xi-xiv.
11. ↑ For the analogy with the turbulence theory or with earthquake research cf. Voit, 2000 and Sornette, 2003.
12. ↑ See Richard Nelson, S. Winter: An Evolutionary Theory of Economic Change . Harvard University Press, Cambridge / MA 1982.
13. ↑ See Philippe Aghion, P. Howitt: Endogenous Growth Theory . MIT Press, Cambridge (MA) 1999.
14. ↑ Quoted in William A. Barnett et al. a. (Ed.): Commerce, Complexity and Evolution . Cambridge University Press, Cambridge 2000, p. 62.
15. ↑ From the English: "Power-Law-Distribution" "
16. ↑ See Vilfredo Pareto: Cours d'économie politique . F. Rouge, Lausanne 1896–1897 (2 volumes)
17. ↑ See Parameswaran Gopikrishnan u. a. (Ed.): Inverse Cubic Law for the Probability Distribution of Stock Price Variations. In: European Journal of Physics B3. 1998.
18. ↑ Cf. Xavier Gabaix et al. a .: A Theory of Large Fluctuations in Stock Market Activity. MIT Press, Cambridge (MA) 2003.
19. ^ E.g. in Fabrizio Lillo, JD Farmer: The Long Memory of the Efficient Market. In: Studies in Nonlinear Dynamics and Econometrics 8 (3). 2004.
20. ↑ See Liu, Cizeau, Meyer, Peng, Stanley: Correlations in economic time series. In: Physica A. A245, pp. 437-440.
21. ^ Cf. Breidt, Crato, de Lima: On the detection and estimation of long memory in stochastic volatility. In: Journal of Econometrics. 83, pp. 325-348.
22. ↑ See Vassilicos, Demos, Tata: No evidence of chaos but some evidence of multifractals in foreign exchange and the stock market. In: Crilly, Earnshaw, Jones (Eds.): Applications of Fractals and Chaos . Springer, Berlin 1993.
23. ↑ Benoit Mandelbrot, Laurent Calvet, Adlai Fischer: A Multifractal Model of Asset Returns . Discussion Papers, Cowles Foundation Yale University, 1997, pp. 1164-1166.
24. ↑ See Calvet, Fisher: Forecasting multifractal volatility. In: Journal of Econometrics 105. 2001, pp. 27-58.
25. ^ Jean Philippe Bouchaud et al. a .: Statistical properties of stock order books: empirical results and models. In: Quantitative Finance 2. 2002.
26. ^ JD Farmer, II Zovko: The power of patience. In: Quantitative Finance 2. 2002.
27. ↑ Cf. Parameswaran Gopakrishnan et al. a .: Scaling of the distributions of fluctuations of financial market indices. In: Physical Review E. 60, 1999, pp 5305-5316.
28. ^ Cf. Rosario Mantegna, E. Stanley: An Introduction to Econophysics: Correlations and Complexity in Finance . Cambridge University Press, Cambridge 2000, p. 88.
29. ↑ Cf. Didier Sornette, A. Johansen, JP Bouchaud: Stock market crashes, precursors and replicas. In: Journal de Physique I 6 (1). Pp. 167-175.
30. ↑ Cf. Didier Sornette: Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press, Princeton 2003.
31. ↑ A summary of the discussion can be found in Lux 2007, pp. 35ff.
32. ^ See Levy and Solomon, 1997.
33. ↑ See Arnab Chatterjee, S. Yarlagadda, BK Chakrabarti (Ed.): Econophysics of Wealth Distributions. Springer, Milan, 2005.
34. ↑ See John Angle: The Surplus Theory of Social Stratification and the Size Distributions of Personal Wealth. In: Social Forces 65 (2). 1986, pp. 293-326.
35. ↑ See Adrian Dragulescu, VM Yakovenko: Gibbs Distribution of Money: A Computer Simulation. In: Journal of Theoretical and Applied Finance 3. 2000.
36. ^ A. Chakraborti, B. Chakrabarti: Statistical Mechanics of Money. In: European Physical Journal B17. 2000.
37. ↑ See Jean Philippe Boucheaud, R. Cont: Herd Behavior and Aggregate Fluctuations in Financial Markets. In: Macroeconomic Dynamics 2. 2000.
38. ↑ See Stanley: Zipf Plots and the Size Distribution of Firms. In: Economic Letters 49 (4) , 1995.
39. ↑ See Stanley: Scaling b Behavior in the Growth of Companies. In: Nature 379, 1996.
40. ↑ See e.g. B. Xavier: Zipf's law for cities: an explanation. In: Quarterly Journal of Economics. 114, 1999.
41. ↑ See e.g. B. Plerou, Amaral, Gopakrishnan, Meyer, Stanley: Similarities between the growth dynamics of university research and competitive economic activities. In: Nature. 400, 1999.
42. ↑ ^{a b} See Preis, Mantegna, 2003.
43. ↑ Mauro Gallegati, Steve Keen, Thomas Lux, Paul Ormerod: Worrying Trends in Econophysics . In: Physica A . tape 370 , 2006, p. 1–6 , doi : 10.1016 / j.physa.2006.04.029 ( paulormerod.com [PDF; accessed December 8, 2012]).
44. ↑ See also the opposite position: Joseph L. McCauley: Response to “Worrying Trends in Econophysics” . Working paper. arxiv : physics / 0606002
45. ↑ Philip Ball: Econophysics: Culture Crash. In: Nature. 441, June 8, 2006, pp. 686-688.
46. ↑ If z. If, for example , they depend on time in contrast to and not explicitly, this should only take into account that they fluctuate comparatively more slowly. ${\displaystyle J_{i,k}}$ ${\displaystyle E_{0}(t)}$ ${\displaystyle H_{i}(t)}$