Increasing market efficiency in the stock markets

Abstract.We study the temporal evolutions of three stock markets; Standard and Poor's 500 index, Nikkei 225 Stock Average, and the Korea Composite Stock Price Index. We observe that the probability density function of the log-return has a fat tail but the tail index has been increasing continuously in recent years. We have also found that the variance of the autocorrelation function, the scaling exponent of the standard deviation, and the statistical complexity decrease, but that the entropy density increases as time goes over time. We introduce a modified microscopic spin model and simulate the model to confirm such increasing and decreasing tendencies in statistical quantities. These findings indicate that these three stock markets are becoming more efficient.

[1]  B. Chakrabarti,et al.  Econophysics of Stock and other Markets , 2006 .

[2]  Victor M. Yakovenko,et al.  Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact , 2004 .

[3]  Robert Haslinger,et al.  Quantifying self-organization with optimal predictors. , 2004, Physical review letters.

[4]  R. Riera,et al.  Truncated Lévy walks and an emerging market economic index , 2001 .

[5]  R. Mantegna,et al.  Empirical investigation of stock price dynamics in an emerging market , 1999 .

[6]  Woo-Sung Jung,et al.  Microscopic spin model for the dynamics of the return distribution of the Korean stock market index , 2006 .

[7]  H. Eugene Stanley,et al.  Scale-Dependent Price Fluctuations for the Indian Stock Market , 2004 .

[8]  Richard W Clarke,et al.  Application of computational mechanics to the analysis of natural data: an example in geomagnetism. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  V. Plerou,et al.  Similarities and differences between physics and economics , 2001 .

[10]  Taisei Kaizoji,et al.  Empirical Laws of a Stock Price Index and a Stochastic Model , 2003, Adv. Complex Syst..

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

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

[13]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[14]  Underlying dynamics of typical fluctuations of an emerging market price index: The Heston model from minutes to months , 2005, physics/0506101.

[15]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[16]  D. Helbing,et al.  Volatility clustering and scaling for financial time series due to attractor bubbling. , 2002, Physical review letters.

[17]  K. Lim,et al.  Ranking market efficiency for stock markets: A nonlinear perspective , 2007 .

[18]  B. M. Tabak,et al.  The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient , 2004 .

[19]  Enrico Enrico,et al.  The Art of Fitting Financial Time Series with Levy Stable Distributions , 2007 .

[20]  Enrico Scalas,et al.  The application of continuous-time random walks in finance and economics , 2006 .

[21]  J. Crutchfield,et al.  Statistical complexity of simple one-dimensional spin systems , 1997, cond-mat/9702191.

[22]  S. Bornholdt,et al.  Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents , 2002, cond-mat/0207253.

[23]  T. Takaishi.  SIMULATIONS OF FINANCIAL MARKETS IN A POTTS-LIKE MODEL , 2005, cond-mat/0503156.

[24]  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 .

[25]  Taisei Kaizoji.  Speculative bubbles and crashes in stock markets: an interacting-agent model of speculative activity , 2000 .

[26]  James P. Crutchfield,et al.  Computational mechanics of cellular automata: an example , 1997 .

[27]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[28]  James P. Crutchfield,et al.  Computational Mechanics: Pattern and Prediction, Structure and Simplicity , 1999, ArXiv.

[29]  Gemunu H. Gunaratne,et al.  An Empirical Model for Volatility of Returns and Option Pricing , 2002, ArXiv.

[30]  Okyu Kwon,et al.  Information flow between composite stock index and individual stocks , 2007, 0708.0063.

[31]  A. Lo,et al.  Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test , 1987 .

[32]  Hang-Hyun Jo,et al.  Complexity analysis of the stock market , 2006, physics/0607283.

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