We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the non-linear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described by a power-law function lacking a typical scale.
LILLO F, RN MANTEGNA (2004). Dynamics of a financial market index after a crash. PHYSICA. A, 338(1-2), 125-134 [10.1016/j.physa.2004.02.034].
Dynamics of a financial market index after a crash
LILLO, Fabrizio;MANTEGNA, Rosario Nunzio
2004-01-01
Abstract
We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the non-linear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described by a power-law function lacking a typical scale.
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