  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 nonlinear 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.
