Power-law relaxation in a complex system: Omori law after a financial market crash

F. Lillo and R. N. Mantegna
Phys. Rev. E 68, 016119 – Published 23 July 2003
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Abstract

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power-law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models.

  • Received 12 December 2001

DOI:https://doi.org/10.1103/PhysRevE.68.016119

©2003 American Physical Society

Authors & Affiliations

F. Lillo1 and R. N. Mantegna1,2

  • 1Istituto Nazionale per la Fisica della Materia, Unità di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
  • 2Dipartimento di Fisica e Tecnologie Relative, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy

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Vol. 68, Iss. 1 — July 2003

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