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Econophysics

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Application of physics to the study of economics

Econophysics is a non-orthodox (in economics) 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. Some of its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics. Econophysics is closely related to social physics.

History

Physicists' interest in the social sciences is not new (see e.g.,); 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. Likewise, Jan Tinbergen, who won the first Nobel Memorial Prize in Economic Sciences in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with Paul Ehrenfest at Leiden University. In particular, Tinbergen developed the gravity model of international trade that has become the workhorse of international economics.

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, to describe the large number of papers written by physicists in the problems of (stock and other) markets, in a conference on statistical physics in Kolkata (erstwhile Calcutta) in 1995 and first appeared in its proceedings publication in Physica A 1996. The inaugural meeting on econophysics was organised in 1998 in Budapest by János Kertész and Imre Kondor. The first book on econophysics was by R. N. Mantegna & H. E. Stanley in 2000.

The almost regular meeting series on the topic include: Econophys-Kolkata (held in Kolkata & Delhi), Econophysics Colloquium, ESHIA/ WEHIA.

In recent years network 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 in European Funded Research Projects as Forecasting Financial Crises and the Harvard-MIT Observatory of Economic Complexity

Basic tools

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

Physics models that have been applied in economics include the kinetic theory of gas (called the kinetic exchange models of markets), percolation models, chaotic models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for earthquake prediction. 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.

For potential games, it has been shown that an emergence-producing equilibrium based on information via Shannon information entropy produces the same equilibrium measure (Gibbs measure from statistical mechanics) as a stochastic dynamical equation which represents noisy decisions, both of which are based on bounded rationality models used by economists. The fluctuation-dissipation theorem connects the two to establish a concrete correspondence of "temperature", "entropy", "free potential/energy", and other physics notions to an economics system. The statistical mechanics model is not constructed a-priori - it is a result of a boundedly rational assumption and modeling on existing neoclassical models. It has been used to prove the "inevitability of collusion" result of Huw Dixon in a case for which the neoclassical version of the model does not predict collusion. Here the demand is increasing, as with Veblen goods, stock buyers with the "hot hand" fallacy preferring to buy more successful stocks and sell those that are less successful, or among short traders during a short squeeze as occurred with the WallStreetBets group's collusion to drive up GameStop stock price in 2021. Nobel laureate and founder of experimental economics Vernon L. Smith has used econophysics to model sociability via implementation of ideas in Humanomics. There, noisy decision making and interaction parameters that facilitate the social action responses of reward and punishment result in spin glass models identical to those in physics.

Quantifiers derived from information theory were used in several papers by econophysicist Aurelio F. Bariviera and coauthors in order to assess the degree in the informational efficiency of stock markets. Zunino et al. use an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This Cartesian representation establish an efficiency ranking of different markets and distinguish different bond market dynamics. It was found that more developed countries have stock markets with higher entropy and lower complexity, while those markets from emerging countries have lower entropy and higher complexity. Moreover, the authors conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. A similar study developed by Bariviera et al. explore the relationship between credit ratings and informational efficiency of a sample of corporate bonds of US oil and energy companies using also the complexity–entropy causality plane. They find that this classification agrees with the credit ratings assigned by Moody's.

Another good example is random matrix theory, which can be used to identify the noise in financial correlation matrices. One paper has argued that this technique can improve the performance of portfolios, e.g., in applied in portfolio optimization.

The ideology of econophysics is embodied in a new probabilistic economic theory and, on its basis, a unified theory of stock markets.

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 for a critique of the Black–Scholes methodology). The Black–Scholes theory can be extended to provide an analytical theory of main factors in economic activities.

Subfields

Various other tools from physics that have so far been used, such as fluid dynamics, classical mechanics and quantum mechanics (including so-called classical economy, quantum economics and quantum finance), and the Feynman–Kac formula of statistical mechanics.

Statistical mechanics

Main article: Feynman–Kac formula

When mathematician Mark Kac attended a lecture by Richard Feynman he realized their work overlapped. Together they worked out a new approach to solving stochastic differential equations. Their approach is used to efficiently calculate solutions to the Black–Scholes equation to price options on stocks.

Quantum finance

Main article: Quantum finance

Quantum statistical models have been successfully applied to finance by several groups of econophysicists using different approaches, but the origin of their success may not be due to quantum analogies.

Quantum economics

The editorial in the inaugural issue of the journal Quantum Economics and Finance says: "Quantum economics and finance is the application of probability based on projective geometry—also known as quantum probability—to modelling in economics and finance. It draws on related areas such as quantum cognition, quantum game theory, quantum computing, and quantum physics." In his overview article in the same issue, David Orrell outlines how neoclassical economics benefited from the concepts of classical mechanics, and yet concepts of quantum mechanics "apparently left economics untouched". He reviews different avenues for quantum economics, some of which he notes are contradictory, settling on "quantum economics therefore needs to take a different kind of leaf from the book of quantum physics, by adopting quantum methods, not because they appear natural or elegant or come pre-approved by some higher authority or bear resemblance to something else, but because they capture in a useful way the most basic properties of what is being studied."

Main results

Econophysics is having some impacts 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 physics of financial markets or original points of view on established models.

Presently, one of the main results of econophysics comprises 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), 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 negligible 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 P ∝ x − 4 , {\displaystyle 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 10 data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away". 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.

As in quantum field theory the "fat tails" can 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. Fat tails can, however, also be due to other phenomena, such as a random number of terms in the central-limit theorem, or any number of other, non-econophysics models. Due to the difficulty in testing such models, they have received less attention in traditional economic analysis.

Criticism

In 2006 economists Mauro Gallegati, Steve Keen, Thomas Lux, and Paul Ormerod, published a critique of econophysics. They cite important empirical contributions primarily in the areas of finance and industrial economics, but list four concerns with work in the field: lack of awareness of economics work, resistance to rigor, a misplaced belief in universal empirical regularity, and inappropriate models.

See also

References

  1. "The Story of Econophysics - Cambridge Scholars Publishing". cambridgescholars.com.
  2. Yale Economic Review, Retrieved October-25-09 Archived 2008-05-08 at the Wayback Machine
  3. "K. Gangopadhyay, Interview of H. E. Stanley on Econophysics (Published in "IIM Kozhikode Society & Management Review", Sage publication (USA), Vol. 2 Issue 2 (July), pp. 73-78 (2013))" (PDF).
  4. Ghosh, Asim (August 26, 2013). "Econophysics Research in India in the last two Decades". arXiv:1308.2191. doi:10.48550/arXiv.1308.2191 – via arXiv.org.
  5. "An Introduction to Econophysics", Cambridge University Press, Cambridge (2000)
  6. "Econophysics of Wealth Distributions", Eds. A. Chatterjee et al., New Economic Windows, Springer, Milan (2005), & the subsequent eight Econophys-Kolkata Conf. Proc. Volumes published in 2006, 2007, 2010, 2011, 2013, 2014, 2015 & 2019 in the New Economic Windows series of Springer
  7. Bikas K Chakrabarti, Anirban Chakraborti, Satya R Chakravarty, Arnab Chatterjee (2012). Econophysics of Income & Wealth Distributions. Cambridge University Press, Cambridge. Bibcode:2013eiwd.book.....C.{{cite book}}: CS1 maint: multiple names: authors list (link)
  8. Didier Sornette (2003). Why Stock Markets Crash?. Princeton University Press.
  9. Kahneman, Daniel; Sibony, Olivier; Sunstein, Cass R. (2021). Noise: A Flaw in Human Judgment. William Collins. ISBN 978-0008308995.
  10. Dixon, Huw (2000). "keeping up with the Joneses: competition and the evolution of collusion". Journal of Economic Behavior and Organization. 43 (2): 223–238. doi:10.1016/s0167-2681(00)00117-7.
  11. Campbell, Michael J. (2016). "Inevitability of Collusion in a Coopetitive Bounded Rational Cournot Model with Increasing Demand". Journal of Mathematical Economics and Finance. 2 (1): 7–20.
  12. Johnson, Joseph; Tellis, G.J.; Macinnis, D.J. (2005). "Losers, Winners, and Biased Trades". Journal of Consumer Research. 2 (32): 324–329. doi:10.1086/432241. S2CID 145211986.
  13. Levine, Matt (18 February 2021). "Congress Wants to Talk About GameStop". Bloomberg.
  14. Michael J. Campbell and Vernon L. Smith (2021). "An elementary humanomics approach to boundedly rational quadratic models". Physica A. 562: 125309. Bibcode:2021PhyA..56225309C. doi:10.1016/j.physa.2020.125309.
  15. Zunino, L., Bariviera, A.F., Guercio, M.B., Martinez, L.B. and Rosso, O.A. (2012). "On the efficiency of sovereign bond markets" (PDF). Physica A: Statistical Mechanics and Its Applications. 391 (18): 4342–4349. Bibcode:2012PhyA..391.4342Z. doi:10.1016/j.physa.2012.04.009. hdl:11336/59368. S2CID 122129979.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  16. Bariviera, A.F., Zunino, L., Guercio, M.B., Martinez, L.B. and Rosso, O.A. (2013). "Efficiency and credit ratings: a permutation-information-theory analysis" (PDF). Journal of Statistical Mechanics: Theory and Experiment. 2013 (8): 08007. arXiv:1509.01839. Bibcode:2013JSMTE..08..007F. doi:10.1088/1742-5468/2013/08/P08007. hdl:11336/2007. S2CID 122829948.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  17. Vasiliki Plerou; Parameswaran Gopikrishnan; Bernd Rosenow; Luis Amaral; Thomas Guhr; H. Eugene Stanley (2002). "Random matrix approach to cross correlations in financial data". Physical Review E. 65 (6): 066126. arXiv:cond-mat/0108023. Bibcode:2002PhRvE..65f6126P. doi:10.1103/PhysRevE.65.066126. PMID 12188802. S2CID 2753508.
  18. ^ Anatoly V. Kondratenko (2015). Probabilistic Economic Theory. Nauka. ISBN 978-5-02-019121-1.
  19. Anatoly V. Kondratenko (2021). Probabilistic Theory of Stock Exchanges. Nauka. ISBN 978-5-02-041486-0.
  20. ^ Jean-Philippe Bouchaud; Marc Potters (2003). Theory of Financial Risk and Derivative Pricing. Cambridge University Press. ISBN 9780521819169.
  21. Bouchaud, J-P.; Potters, M. (2001). "Welcome to a non-Black-Scholes world". Quantitative Finance. 1 (5): 482–483. doi:10.1080/713665871. S2CID 154368053.
  22. ^ Chen, Jing (2015). The Unity of Science and Economics: A New Foundation of Economic Theory. Springer. doi:10.1007/978-1-4939-3466-9. ISBN 978-1-4939-3464-5.
  23. ^ Oksendal, Bernt. Stochastic differential equations: an introduction with applications. Springer Science & Business Media, 2013.
  24. Kac, Mark (1987). Enigmas of Chance: An Autobiography. University of California Press. pp. 115–16. ISBN 0-520-05986-7.
  25. Paolo Brandimarte (6 June 2013). "Chapter 1. Motivation". Numerical Methods in Finance and Economics: A MATLAB-Based Introduction. John Wiley & Sons. ISBN 978-1-118-62557-6.
  26. Arioli, Gianni; Valente, Giovanni (October 2021). "What Is Really Quantum in Quantum Econophysics?". Philosophy of Science. 88 (4): 665–685. doi:10.1086/713921. ISSN 0031-8248.
  27. Rickles, Dean (December 2007). "Econophysics for philosophers". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 38 (4): 948–978. Bibcode:2007SHPMP..38..948R. doi:10.1016/j.shpsb.2007.01.003.
  28. Orrell, David; Haven, Emmanuel; Hawkins, Raymond J. (2024-01-17). "What is Quantum Finance and Economics?". Quantum Economics and Finance. 1: 3–4. doi:10.1177/29767032231210519. ISSN 2976-7032.
  29. Orrell, David (2024-03-08). "Quantum Economics and Physics". Quantum Economics and Finance. doi:10.1177/29767032241237547. ISSN 2976-7032.
  30. Enrico Scalas (2006). "The application of continuous-time random walks in finance and economics". Physica A. 362 (2): 225–239. Bibcode:2006PhyA..362..225S. doi:10.1016/j.physa.2005.11.024.
  31. Y. Shapira; Y. Berman; E. Ben-Jacob (2014). "Modelling the short term herding behaviour of stock markets". New Journal of Physics. 16 (5): 053040. Bibcode:2014NJPh...16e3040S. doi:10.1088/1367-2630/16/5/053040.
  32. The physicists noted the scaling behaviour of "fat tails" through a letter to the scientific journal Nature by Rosario N. Mantegna and H. Eugene Stanley: Scaling behavior in the dynamics of an economic index, Nature Vol. 376, pages 46-49 (1995)
  33. ^ See for example Preis, Mantegna, 2003.
  34. Gallegati, Mauro; Keen, Steve; Lux, Thomas; Ormerod, Paul (2006-10-01). "Worrying trends in econophysics". Physica A: Statistical Mechanics and Its Applications. Econophysics Colloquium. 370 (1): 1–6. Bibcode:2006PhyA..370....1G. doi:10.1016/j.physa.2006.04.029. ISSN 0378-4371.
  35. Philip Ball (2006). "Econophysics: Culture Crash". Nature. 441 (7094): 686–688. Bibcode:2006Natur.441..686B. CiteSeerX 10.1.1.188.8120. doi:10.1038/441686a. PMID 16760949. S2CID 4319192.

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