**Yougui Wang, Jinshan Wu, Zengru Di
1. Department of System Science at School of Management,
Beijing
Normal University, Beijing, 100875, P.R.China
2. Department of Physics, Simon Fraser University, Burnaby, B.C.
Canada, V5A 1S6**

Econophysics is a new area developed recently by the cooperation
between economists, mathematicians and physicists. It's not a tool
to predict future prices of stocks and exchange rates. It applies
idea, method and models in Statistical Physics and Complexity to
analyze data from economical phenomena. In this talk, three
examples from three active main topics in Econophysics are
presented first. Then using these examples, we analyze the role of
Physics in Econophysics. Some comments and emphasis on Physics of
Econophysics are included.

- Introduction
- Three main topics of Econophysics
- Fluctuation of stock prices and exchange rates
- Distribution of firm sizes, GDP, personal income and wealth
- Complex Networks of economy systems

- Why is Econophysics?

- Conclusion - Is Econophysics a subject of Physics?
- Acknowledgement
- Bibliography
- About this document ...

Also because of the plenty data records of different systems in our economy behavior, it's a treasure to physicists, especially to the one being interested in Complex Systems, in which many subsystems and many variables interact together. And the development of Economics also provide many open questions, like stock price, exchange rate and risk management, which may require technics dealing with mass data and complex systems.

Physics tries to construct a picture of the movement of the whole nature. Mechanism is the first topic cared by physicists. So trying to describe and understand the phenomena is the first step of econophysicists facing the mass data in economical phenomena. Till now, we have to say, the most works in Econophysics are empirical study of different phenomena to discover some universal or special laws, and also some initial effort about models and mechanism.

Therefor, in this talk, we will begin with three examples of empirical works in Econophysics, and discuss very shortly about the corresponding models and mechanism. Focus will be on the Physics of Econophysics, to present the power of Physics to Econophysics and some benefit which Physics will get from Econophysics.

A typical time series of stock price, SP500 index, denoted as , is showed in figure 1. Actually SP500 is a stock index, which is a weighted mean value of stocks in a market, can be used as a indicator of stock price. Some papers use the data of indexes, some use individual stock, and also some paper investigate all stocks in a market as an ensemble of stocks. In this talk, we just use analysis of individual stock as examples.

Because economy is in growth, so the time series of stock price
has a long term trend to increase. This means it's nonstationary.
So other than the original price, other quantities like different
and return may be better to use as analysis object. The difference
is defined as

(1) |

(2) |

Most works use return as object time series. The figures in the lower part of figure 1 show examples of , while the last one is a Gaussian noise signal for comparison.

A statistical analysis of one time series can be classified as two parts, the distribution properties which dismiss the time information, and the autocorrelation analysis which mainly takes time into account.

Another distribution properties is about the volatility of stock,
which is related with risk. So its characters is important for
risk management. Usually it's defined by local variation,

(3) |

(4) |

(5) |

(6) |

In figure 4, the autocorrelation functions of return and volatility are plotted together. We can find an exponential drop off in return with a time scale of minute, while a power law decrease in volatility without a finite time scale. Think about this phenomenon, a time series almost without an autocorrelation, but a extremely high autocorrelation in absolute value, or local variation. It's amazing. The fast dropping off guarantee the validness of Efficient Market Hypothesis, while the long time autocorrelation in volatility make it possible to construct a theory of risk management. So such works will boost the development of risk management, even a reformation.

(7) |

From the above results, it seems that stock price is only determined by transaction volume. But it's sad to say, the transaction volume is also decided by price. No direct way to predict transaction volume. It should be decided together with price by other predictable or known variables. So let's say if we have only one stock, and the whole history of this stock is already known, the achievement and activity of the enterprise is also predictable by other ways, and so is the external economy environment, at least in a statistical way, which means if they are random variables we know the distribution and correlation, in such condition, is the future of this stock determinant, and is it predictable or chaotic? Or at least we can reproduce the similar data with the same statistical characters as the empirical data? If it's possible, what's the central variables, and how it can be generalized into a stock ensemble, not only one stock?

The first idea here is activities of all stockholder are effected each other. Such interaction maybe is indirectly through the price and market, or by external way such as personal relationship. As a tradition in Physics, a first approximation is treat every stockholder independently, so they will only effected each other through market. Like in spin model, every stockholder will has a unit volume can buy or sell every time. Buying will improve the price while selling lowers the price. Everyone is trying to make more money in this game. So till now, a toy model has been constructed for mechanism of stock price. When the detail of benefit evaluation of every player and the effect on price by one unit volume is set, this toy model will evolute in its own way, of course when some specific behavior of all external variables are also settled down.

Although it's only a toy model, we also can test some fundamental knowledge, such as benefit and rational agent, and also try different form of external variables. For example, we can take for granted that external variables are random signals with fixed distribution and without autocorrelation of any order. So our task will be how can we construct our model to reproduce the autocorrelation behavior in empirical study from no autocorrelation input external data.

And then, if the output data is totally incomparable, maybe we have to add something we dismissed, like the relation between stocks. You know a phone call from your close friend may change your decision. So it's very possible we have to take such interaction into consideration. The model in [10], is a representative one of such toy models. Although many different interaction forms we can try, or even we can coevolute the interaction strength together with the stock price, it's possible that the output data is still incomparable with empirical one. Then, we will have to include the interaction between different stocks, and maybe further more a coevolution system including the behavior of enterprises.

Oh, no, wait a minute, this is not on the way of physics now. More and more variables, more and more subsystems, uglier and uglier picture. It shouldn't. The Physics of Complex System tells us maybe only a few ones rule the system. So the toy model maybe imply something valuable. Now we come back to empirical study and toy model, but in another way, the way keeping Physics in mind.

Similar results have been get for GDP of countries all over the world. Power law distribution of GDP per capita of different counties has been revealed in [27].

For individual such distribution can be analyzed by personal income or wealth. A typical result[29,30] is shown in figure 7. The lower income seems like exponential distribution while the higher part is power law. From experience of ideal gas, we know, the equilibrium energy distribution of a random exchange system is exponential. So maybe in the lower income community, the cooperation and competition between individuals is in a way similar with random exchange. But for the higher income part, different interaction like preferential attachment part more important role.

(8) |

(9) |

(10) |

(11) |

(12) |

A recent such development is the web of trade[14,15], in which vertexes are the countries and links are the inport/outport relation. The basic structure and efficiency has been analyzed, like high clustering coefficient, scale-free degree distribution.

Another widely used network of economy system is the interaction between stock agents. Every stockholder is a vertex in the network, and the effect from decision of one agent to another is a directed link from the former vertex to the later. So the network acts as a whole system to drive the stock price. The geometrical character of such network will have some important effects on the dynamical behavior of stock price. Therefor, such investigation maybe will reveal the interaction pattern between stock agents.

The third proposed works about network of economy systems is the network analysis of product input/output table. Like the Predator-Prey Relationships in food web, every product made from other products or raw materials, and also become input of other products. So the input/output relationship between products forms a network. Actually the input/output table analysis in Economics has the same spirit but in a highly clustered level and asking for different questions. So, although a database of product relation is what we need, a clustered group product relation data set will also be able to be used here as an beginning analysis of basic structure characters. And further works will require detailed data on input/output relation of products.

Construction and analysis of such clustered product network is in progress[36]. Characters on degree distribution, clustering coefficient, weight and weight distribution, average shortest distance have been gotten, but questions about the universality of such properties need to be tested on more networks. The links between products can be regarded as technology. So a score analysis such as link betweenness will show the relative importance of different technics, therefor it may imply some new direction of development of technology. Further questions about the robustness of such networks can be asked as how many total product will be lost if one or several inter-products were in shortage, or when the resource distribution was changed, or as how many total product will be lost when one or several link (technics) were dismissed, or inversely, if a new link was invented how many product will grow in total. Such investigation will relate traditional questions in economics such as resource allocation, social welfare, and effect of new technology with network analysis of product. It can have a far-reaching effect both on economics and network analysis.

Another central analysis method transplanted from Physics is Data Collapse and Universality. If relation curves from different systems can be collapsed onto a master curve by scaling, it's very possible to find some common mechanism from such systems. And if an empirical or theoretical relation is independent on time period, some different detail of objects, it's called universality. When a universal law is found for different systems, the systems must be equivalent in some ways. So it implies common mechanism and others can be understood if we know one of them very well. Therefor, it open a new way to investigate such systems, especially when some models with similar properties in Physics and other fields can be used here as a reference model for economy phenomena.

(13) |

Such application gives some reasonable results, although it may be not totally equivalent with assumption in Economics, where every agent must stay on its maximum point, not a distribution function. In Mechanics, the status of physical object is determined by Newton's equations or minimum action principle, but for a many-body system in Statistical Mechanics, ensemble distribution is used instead. Although it's not deduced from first principle, it works widely. Maybe similar approach can be developed in Economics.

Ideal gas is another reference model widely used in Econophysics[]. In a first order approximation model of competition and cooperation between firms, or between individuals, every agent can be regarded as random exchange wealth with each other, like random exchange energy in ideal gas. So the equilibrium distribution will take the exponential form. It's amazing that the central part of personal wealth is actually exponential form. Further possible model can be generalized random interaction model, including not random exchange, but also random increase or decrease process, or extended model with bias exchange model, like preferential exchange, in which rich one has higher probability to get richer.

Like DFA method proposed by researchers in Statistical Physics from works in DNA sequence and physiologic signals, new technics can also be invented from Econophysics. Hopefully, not only technics, but also concepts and fundamental approach may also be proposed.

For instance, effect of geometrical property such as dimension and curvature on dynamical behavior is an important question in Physics. Actually it's widely studied in Physics including Relativity, Quantum Physics and especially Phase Transition and Critical Phenomena. So if geometrical quantities can be defined in Complex System, and the effect on dynamical process is known, it will partially predictable just through grasping the geometrical properties of such systems. For example, in principle, the make-from relationship between all products is tractable. So the network can be explicitly constructed, and even part of the history is known, like the things changed when reformation of technics happened. So Economics provide some nearly perfect treasure for Physics. And further more, the special character of such network will definitely require new quantities or technics to describe the effect. This will maybe boost the development of Physics.

Economics is a science of human behavior, but it's fortunate that Economics is not totally a science of human creativity and inspiration like fine art. This means that some part, even most part according mathematicians working in Economics, of Economics can be modelled in an abstract or mathematical form. It's interesting to point out that it's Physics the most famous masterpiece applying Mathematics into nature, not any other field of Applied Mathematics. So it's natural to incorporate Physics into Economics like to imitate masterpieces.

And through such exploration, it's possible that Physics will be widely used in social science. This will greatly extend the scope of Physics, and maybe will help Physics to deal with some hard topic such as turbulence, or more general complex systems.

- 1
- R. N. Mantegna and H. E. Stanley,
*An Introduction to Econophysics: Correlations and Complexity in Finance*(Cambridge University Press, Cambridge, England, 1999). - 2
- J.-P. Bouchaud and M. Potters,
*Theory of Financial Risk*(Cambridge University Press, Cambridge, England, 1999). - 3
- R. Cont, Empirical properties of asset returns: stylized facts and statistical issues, Quantitive Finance,
**1**, 223-236(2001). - 4
- H.E. Stanley, P. Gopikrishnan, V. Plerou, L.A.N. Amaral, Quantifying uctuations in economic systems by adapting methods of statistical physics, Physica A
**287**, 339-361(2000). - 5
- P. Gopikrishman, V. Plerou, Y.liu, L.A.N. Amaral, X. Gabaix and H.E. Stanley, Scaling and correlation in financial time series, Physica A
**287**, 362-373(2000) - 6
- V. Plerou, P. Gopikrishman, L.A.N. Amaral, M. Meyer and H.E. Stanley, Scaling of the distribution of financial market indices, Phys. Rev. E
**60**, 5305-5316(1999). - 7
- V. Plerou, P. Gopikrishman, L.A.N. Amaral, M. Meyer and H.E. Stanley, Scaling of the price fluctuations of the individual companies, Phys. Rev. E
**60**, 6519-6529(1999). - 8
- Rogério L. Costa, G.L. Vasconcelos, Long-range correlations and nonstationarity in the Brazilian stock market, Physica A
**329**, 231-248(2003). - 9
- Y. Liu, P. Gopikrishman, P. Cizeau, M. Meyer, C. Peng and H.E. Stanley, Statistical properties of the volatility of price fluctuations, Phys. Rev. E
**60**, 1390-1400(1999). - 10
- A. Krawiecki, J.A. Holyst and D. Helbing, Volatility clustering and scaling for financial time series due to attactor bublling, Phys. Rev. Lett.
**89**, 158701 (2002). - 11
- M. Raberto, R. Gorenflo, F. Mainardi, E. Scalas, Scaling of the waiting-time distribution in tick-by-tick financial data (Poster presented during the international workshop Economics Dynamics from the Physics Point of View held in Bad Honnef (Germany) on March 2000).
- 12
- L. Sabatelli, S. Keating, J. Dudley, and P. Richmond, Waiting time distributions in financial markets, Eur. Phys. J. B
**27**, 273-275(2002). - 13
- E. Scalas, R. Gorenflo, F. Mainardi, Fractional calculus and continuous-time finance, Physica A
**284**, 376-384 (2000). - 14
- M. A. Serrano and M. Boguna, Topology of the world trade web, Phys. Rev. E
**68**,015101(2003). - 15
- X. Li, Y.Y. Jin, and G. Chen, Complexity and synchronization of the World trade Web, Physica A
**328**, 287-296(2003). - 16
- F. Lillo, J.D. Farmer and R.N. Mantagna, Master curve for price-impact function, Nature
**421**, 129-130(2003). - 17
- V. Plerou, P. Gopikrishman and H.E.Stanley, Quantify stock-price response to demand fluctuations, Phys. Rev. E
**66**, 027104(2002). - 18
- F. Lillo and R. N. Mantegna, Ensemble properties ofsecurities traded in the NASDAQ market, Physica A
**299**, 161-167(2001). - 19
- F. Lillo and R.N. Mantagna, Variety and volatility in financial markets, Phys. Rev. E
**62**, 6126-6134(2000). - 20
- J.R. Iglesias, S. Goncalves, S. Pianegonda, J.L. Vega and G. Abramson, Wealth redistributioninour small world, Physica A
**327**, 12-17 (2003). - 21
- M. Stanley, S. Buldyrev, S. Havlin, R. Mantegna, M. Salinger, H.E. Stanley, Zipf Plot and the Size Distribution of Firms. Economics Letters
**49**, 453-457. - 22
- R.L. Axtell, Zpif distribution of U.S. firm sizes, Sience,
**293**, 1818-1820(2001). - 23
- L.A.N. Amaral, S.V. Buldyrev, H. Leschhorn, P. Maass, M. A. Salinger, H.E. Stanley and M.H.R. Stanley, Scaling bahavior in Economics: I. empirical results for company, J. Phys. I France
**7**, 621-633(1997). - 24
- J.J. Ramsden and Gy. Kiss-Haypál, Company size distribution in different countries, Physica A
**277**, 220-227(2000). - 25
- L.A.N. Amaral, S.V. Buldyrev, S. Havlin, M.A. Salinger and H.E. Stanley, Power law scaling for a system interacting units with complex internal structure, Phys. Rev. Lett
**80**, 1385-1388(1998). - 26
- Y. Lee, L.A.N. Amaral, D. Canning, M. Meyer, and H.E. Stanley, Universal Features in the Growth Dynamics of Complex Organizations, Phys. Rev. Lett.
**81**, 3275(1998). - 27
- Di Guilmi, Corrado, Edoardo Gaffeo, and Mauro Gallegati, Power Law Scaling in the World Income Distribution, Economics Bulletin, Vol.
**15**, No. 6 pp. 1-7(2003). - 28
- D. Canning , L.A.N. Amaral , Y. Lee , M. Meyer , H.E. Stanley, Scaling the volatility of GDP growth rates, Economics Letters
**60**, 335-341(1998). - 29
- A.A. Dragulescu and V.M. Yahovenko, Exponential and power-law probability distributions of wealth and income in the United Kingdom and The Unite States, Physica A
**299**, 213-221(2001). - 30
- A.A. Dragulescu and V.M. Yahovenko, Evidence for the exponential distribution of income in the USA, Eur. Phys. J. B
**20**, 585-589(2001). - 31
- Taisei Kaizoji, Scaling behavior in land markets, Physica A
**326**, 256-264(2003). - 32
- A.A. Dragulescu and V.M. Yahovenko, Statistical mechanics of money, Eur. Phys. J. B
**17**, 723-729(2000). - 33
- J.L. McCauley and G.H. Gunaratne, An empirical model of volatility of returns and option pricing, Physica A
**329**, 178-198(2003). - 34
- G. Bonanno, G. Caldarelli, F. Lillo, and R.N. Mantegna,Topology of correlation based minimal spanning trees in real and model markets, arXiv:cond-mat/0211546 (2002).
- 35
- Peng C-K, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. Phys Rev E 1994;49:1685-1689.
- 36
- Klaus, Jinshan Wu, Zengru Di, and Jiawei Chen, Network analysis of physical input and output tables, in prepairation.
# About this document ...

**Physics of Econophysics**This document was generated using the

**LaTeX**2`HTML`translator Version 2002 (1.62)Copyright © 1993, 1994, 1995, 1996, Nikos Drakos, Computer Based Learning Unit, University of Leeds.

Copyright © 1997, 1998, 1999, Ross Moore, Mathematics Department, Macquarie University, Sydney.The command line arguments were:

**latex2html**`Review`The translation was initiated by Jinshan Wu on 2004-01-01

This is a review paper with some new idea included for further usage for Di's group at BNU.

Anyone who is interested in such works can contact with Prof. Di by zdi@bnu.edu.cn