Topology of correlation-based minimal spanning trees in real and model markets.

We compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the New York Stock Exchange during a 12-year trading period with the one obtained from surrogated data simulated by using simple market models. We find that the empirical tree has features of a complex network that cannot be reproduced, even as a first approximation, by a random market model and by the widespread one-factor model.

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

[2]  K. Pearson.  Biometrika , 1902, The American Naturalist.

[3]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[4]  J. Gower.  Some distance properties of latent root and vector methods used in multivariate analysis , 1966 .

[5]  Mathew D. Penrose.  The random minimal spanning tree in high dimensions , 1996 .

[6]  A. Lo,et al.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1996, Macroeconomic Dynamics.

[7]  Alessandro Flammini,et al.  Universality Classes of Optimal Channel Networks , 1996, Science.

[8]  宮脇 卓.  John Y.Campbell,Andrew W.Lo,A.Craig MacKinlay著「The Econometrics of Financial Markets」 , 1997 .

[9]  D. Saad.  Europhysics Letters , 1997 .

[10]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[11]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[12]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[13]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[14]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

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

[16]  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 .

[17]  F. Lillo,et al.  High-frequency cross-correlation in a set of stocks , 2000 .

[18]  G. Caldarelli,et al.  The fractal properties of Internet , 2000, cond-mat/0009178.

[19]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[20]  Nicolas Vandewalle,et al.  Non-random topology of stock markets , 2001 .

[21]  A. Rinaldo,et al.  Fractal River Basins , 2001 .

[22]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[23]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.