Econophysics: can physicists contribute to the science of economics?

How can computational physicists contribute to the search for solutions to the puzzles posed by modern economics that economists themselves cannot solve? An approach-not very commonly used in economics-is to begin empirically, with real data that you can analyze in some detail, but without prior models. In economics, a great deal of real data is available. If you, moreover, have at your disposal the tools of computational physics and the computing power to carry out any number of approaches, this abundance of data is a great advantage. A careful analysis of any system involves studying the propagation of correlations from one unit of the system to the next. We learned that these correlations propagate both directly and indirectly. At one time, it was imagined that scale-free phenomena are relevant to only a fairly narrow slice of physical phenomena. However, the range of systems that apparently display power-law and hence scale-invariant correlations has increased dramatically in recent years. Such systems range from base-pair correlations in noncoding DNA, lung inflation, and interbeat intervals of the human heart, to complex systems involving large numbers of interacting subunits that display free will. In particular, economic time series, e.g., stock market indices or currency exchange rates, depend on the evolution of a large number of strongly interacting systems far from equilibrium, and belong to the class of complex evolving systems. Thus, the statistical properties of economic time series have attracted the interests of many physicists.

[1]  P. A. Prince,et al.  Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics , 1996 .

[2]  J. M. G. Vilar,et al.  Scaling concepts in periodically modulated noisy systems , 1997 .

[3]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[4]  Rosario N. Mantegna,et al.  Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena , 1997 .

[5]  Dietrich Stauffer Can percolation theory be applied to the stock market , 1998 .

[6]  P. Gopikrishnan,et al.  Inverse cubic law for the distribution of stock price variations , 1998, cond-mat/9803374.

[7]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Dietrich Stauffer,et al.  FUNDAMENTAL JUDGEMENT IN CONT-BOUCHAUD HERDING MODEL OF MARKET FLUCTUATIONS , 1999 .

[9]  H. Stanley,et al.  Modelling urban growth patterns , 1995, Nature.

[10]  J. S. Andrade,et al.  Modeling urban growth patterns with correlated percolation , 1998, cond-mat/9809431.

[11]  Marcel Ausloos,et al.  The crash of October 1987 seen as a phase transition: amplitude and universality , 1998 .

[12]  Kenji Okuyama,et al.  Country Dependence on Company Size Distributions and a Numerical Model Based on Competition and Cooperation , 1998 .

[13]  T. Guhr,et al.  RANDOM-MATRIX THEORIES IN QUANTUM PHYSICS : COMMON CONCEPTS , 1997, cond-mat/9707301.

[14]  T. Lux The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions , 1998 .

[15]  Albert-László Barabási,et al.  Avalanches and power-law behaviour in lung inflation , 1994, Nature.

[16]  Rosario N. Mantegna,et al.  Turbulence and financial markets , 1996, Nature.

[17]  Stanley,et al.  Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. , 1994, Physical review letters.

[18]  H. Eugene Stanley,et al.  Universal features in the growth dynamics of complex organizations , 1998, cond-mat/9804100.

[19]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[20]  J. Peinke,et al.  Turbulent cascades in foreign exchange markets , 1996, Nature.

[21]  Didier Sornette,et al.  The Black-Scholes option pricing problem in mathematical finance : generalization and extensions for a large class of stochastic processes , 1994 .

[22]  Sergei Maslov,et al.  Probability Distribution of Drawdowns in Risky Investments , 1998 .

[23]  Koichi Hamada,et al.  Statistical properties of deterministic threshold elements - the case of market price , 1992 .

[24]  M. Shlesinger,et al.  Comment on "Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight" , 1995, Physical review letters.

[25]  M. Marsili,et al.  Interacting Individuals Leading to Zipf's Law , 1998, cond-mat/9801289.

[26]  Dietrich Stauffer,et al.  Crossover in the Cont–Bouchaud percolation model for market fluctuations , 1998 .

[27]  Misako Takayasu,et al.  STABLE INFINITE VARIANCE FLUCTUATIONS IN RANDOMLY AMPLIFIED LANGEVIN SYSTEMS , 1997 .

[28]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[29]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[30]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[31]  D. Sornette,et al.  ”Direct” causal cascade in the stock market , 1998 .

[32]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[33]  M. Marsili,et al.  A Prototype Model of Stock Exchange , 1997, cond-mat/9709118.

[34]  P. Cizeau,et al.  Statistical properties of the volatility of price fluctuations. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  H. Eugene Stanley,et al.  Dynamics of North American breeding bird populations , 1998, Nature.

[36]  David Rahman,et al.  Applications of physics in financial analysis , 2001 .

[37]  Sergey V. Buldyrev,et al.  Scaling behavior in economics: II. Modeling of company growth , 1997, cond-mat/9702085.

[38]  S. Havlin,et al.  Power law scaling for a system of interacting units with complex internal structure , 1998 .

[39]  H. Stanley,et al.  The relationship between liquid, supercooled and glassy water , 1998, Nature.

[40]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[41]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[42]  B. Mandelbrot The Variation of Certain Speculative Prices , 1963 .

[43]  Andrew G. Glen,et al.  APPL , 2001 .

[44]  Shlomo Havlin,et al.  Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis , 1996, Nature.

[45]  F. Dyson Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[46]  P. Cizeau,et al.  CORRELATIONS IN ECONOMIC TIME SERIES , 1997, cond-mat/9706021.

[47]  P. A. Mello,et al.  Random matrix physics: Spectrum and strength fluctuations , 1981 .

[48]  Rama Cont,et al.  Scale Invariance and Beyond , 1997 .

[49]  B. M. Fulk MATH , 1992 .

[50]  L. Amaral,et al.  Scaling behaviour in the growth of companies , 1996, Nature.

[51]  Jean-Philippe Bouchaud,et al.  Mutual attractions: physics and finance , 1999 .

[52]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[53]  C. Peng,et al.  Long-range correlations in nucleotide sequences , 1992, Nature.

[54]  Allan Timmermann Scales and stock markets , 1995, Nature.

[55]  Didier Sornette LARGE DEVIATIONS AND PORTFOLIO OPTIMIZATION , 1998 .

[56]  Sergei Maslov,et al.  Dynamical optimization theory of a diversified portfolio , 1998 .

[57]  P. Cizeau,et al.  Volatility distribution in the S&P500 stock index , 1997, cond-mat/9708143.

[58]  Marcel Ausloos,et al.  Sparseness and roughness of foreign exchange rates , 1998 .

[59]  R. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[60]  D. Sornette,et al.  Stock Market Crashes, Precursors and Replicas , 1995, cond-mat/9510036.

[61]  Sergey V. Buldyrev,et al.  Scaling behavior in economics: I Epirical results for company growth , 1997, cond-mat/9702082.

[62]  K. S. Lee,et al.  Reversal of current through calcium channels in dialysed single heart cells , 1982, Nature.

[63]  Rama Cont,et al.  Service de Physique de l’État Condensé, Centre d’études de Saclay , 1997 .

[64]  R. Mantegna Lévy walks and enhanced diffusion in Milan stock exchange , 1991 .

[65]  Jean-Raymond Abrial,et al.  On B , 1998, B.

[66]  Zhang,et al.  Products of random matrices and investment strategies. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[67]  Dietrich Stauffer,et al.  A generalized spin model of financial markets , 1999 .

[68]  S. Solomon,et al.  A microscopic model of the stock market: Cycles, booms, and crashes , 1994 .

[69]  Yicheng Zhang,et al.  On the minority game: Analytical and numerical studies , 1998, cond-mat/9805084.

[70]  Rama Cont,et al.  A Langevin approach to stock market fluctuations and crashes , 1998 .

[71]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[72]  L. Bachelier,et al.  Théorie de la spéculation , 1900 .

[73]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[74]  M. Dacorogna,et al.  A geographical model for the daily and weekly seasonal volatility in the foreign exchange market , 1993 .

[75]  Guido Caldarelli,et al.  Scaling in currency exchange , 1997 .

[76]  R. Mantegna,et al.  Systematic analysis of coding and noncoding DNA sequences using methods of statistical linguistics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[77]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[78]  Dietrich Stauffer,et al.  MONTE CARLO SIMULATION OF VOLATILITY CLUSTERING IN MARKET MODEL WITH HERDING , 1999 .

[79]  S. Solomon,et al.  Dynamical Explanation For The Emergence Of Power Law In A Stock Market Model , 1996 .

[80]  M. Ausloos,et al.  Multi-affine analysis of typical currency exchange rates , 1998 .

[81]  P. Levy Théorie de l'addition des variables aléatoires , 1955 .

[82]  J. Bouchaud,et al.  Rational Decisions, Random Matrices and Spin Glasses , 1998, cond-mat/9801209.

[83]  Didier Sornette,et al.  A hierarchical model of financial crashes , 1998 .

[84]  Koponen,et al.  Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[85]  Thomas Lux,et al.  Long-term stochastic dependence in financial prices: evidence from the German stock market , 1996 .

[86]  T. Lux Time variation of second moments from a noise trader/infection model , 1997 .

[87]  Charles Gide,et al.  Cours d'économie politique , 1911 .