6533b86efe1ef96bd12cb4b1
RESEARCH PRODUCT
Power-law relaxation in a complex system: Omori law after a financial market crash
Fabrizio LilloRosario N. Mantegnasubject
Statistical Finance (q-fin.ST)Statistical Mechanics (cond-mat.stat-mech)Stochastic volatilityStochastic processFOS: Physical sciencesQuantitative Finance - Statistical FinanceAbsolute valueCrashProbability density functionPower lawFOS: Economics and businessLawEconometricsRelaxation (physics)Time seriesCondensed Matter - Statistical MechanicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-07-23 | Physical Review E |