Criticality and Phase Transition in Stock-Price Fluctuations

Ken Kiyono, Zbigniew R. Struzik, and Yoshiharu Yamamoto
Phys. Rev. Lett. 96, 068701 – Published 13 February 2006

Abstract

We analyze the behavior of the U.S. S&P 500 index from 1984 to 1995, and characterize the non-Gaussian probability density functions (PDF) of the log returns. The temporal dependence of fat tails in the PDF of a ten-minute log return shows a gradual, systematic increase in the probability of the appearance of large increments on approaching black Monday in October 1987, reminiscent of parameter tuning towards criticality. On the occurrence of the black Monday crash, this culminates in an abrupt transition of the scale dependence of the non-Gaussian PDF towards scale-invariance characteristic of critical behavior. These facts suggest the need for revisiting the turbulent cascade paradigm recently proposed for modeling the underlying dynamics of the financial index, to account for time varying—phase transitionlike and scale invariant–critical-like behavior.

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  • Received 14 April 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.068701

©2006 American Physical Society

Authors & Affiliations

Ken Kiyono, Zbigniew R. Struzik, and Yoshiharu Yamamoto*

  • Educational Physiology Laboratory, Graduate School of Education, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • *Electronic address: yamamoto@p.u-tokyo.ac.jp

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Issue

Vol. 96, Iss. 6 — 17 February 2006

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