title: Power-law relaxation in a complex system: Omori law after a financial market crash.
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.
authors.affiliation: Istituto Nazionale per la Fisica della Materia, Unità di Palermo, Viale delle Scienze, I-90128 Palermo, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Lillo
authors.forename: R N
authors.initials: RN
authors.lastname: Mantegna