Journal of the Korean Physical Society

Korean Physical Society (한국물리학회)
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Scale-Free Network in Stock Markets

Kim H.-J.;Kim I.-M.;Lee Y.;Kahng B.

  • Published : 2002.06.01
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Abstract

We study the cross-correlations in stock price changes among the S&P 500 companies by introducing a weighted random graph, where all vertices (companies) are fully connected via weighted edges. The weight of each edge is distributed in the range of [-1,1] and is given by the normalized covariance of the two modified returns connected, where the modified return means the return minus the mean over all companies. We define an influence-strength at each vertex as the sum of the weights on the edges incident upon that vertex. Then we find that the influence-strength distribution in its absolute magnitude |$q$| follows a power-law, $P(|q|){\sim}|q|^{-\delta}$, with exponent ${\delta} {\approx} 1.8(1)$.

Keywords

References

  1. Science v.284 N. Goldenfeld;L. P. Kadanoff
  2. Random Graphs B. Bollobas
  3. Publ. Math. Inst. Hung. Acad. Sci. Ser. A v.5 P. Erdos;A. Renyi
  4. Science v.286 A.-L. Barabasi;R. Albert
  5. J. Korean Phys. Soc. v.38 H.-J. Kim;In-mook Kim
  6. Phys. Rev. E v.62 H.-J. Kim;In-mook Kim;J. M. Kim
  7. cond-mat/0106096 R. Albert;A-L. Barabaasi
  8. cond-mat/0106144 S. N. Dorogovtsev;J. F. F. Mendes
  9. Nature v.398 E. L. Berlow
  10. Phys. Rev. Lett. v.86 S. H. Yook;H. Jeong;A.-L. Barabasi;Y. Tu
  11. Applied Nonlinear Dynamics and Stochastic Systems near the Millennium R. N. Mantegna;J. B. Kadtke(ed.);A. Bulsara(ed.)
  12. Science v.284 W. B. Arthur
  13. Comp. Comm. Rev. v.29 M. Faloutsos;P. Faloutsos;C. Faloutsos
  14. Nature v.401 R. Albert;H. Jeong;A.-L. Barabasi
  15. Nature v.407 H. Jeong;B. Tombor;R. Albert;Z. N. Oltvani;A.-L. Barabasi
  16. cond-mat/0009245 N. Vandewalle;F. Brisbois;X. Tordoir
  17. Introduction to Econophysics : Correlations and Complexity in Finance R. N. Mantegna;H. E. Stanley
  18. Theory of Financial Risks : From Statistical Physics to Risk Management J-P. Bouchaud;M. Potters
  19. Phys. Rev. Lett. v.83 L. Laloux;P. Cizeau;J.-P. Bouchaud;M. Potters
  20. Phys. Rev. Lett. v.83 V. Plerou;P. Gopikrishnan;B. Rosenow;L. A. N. Amaral;H. E. Stanley
  21. Phys. Rev. E v.61 J. D. Noh
  22. Eur. Phys. J. B v.11 R. N. Mantegna
  23. Phys. Rev. E v.62 G. Bonanno;N. Vandewalle;R. N. Mantegna