  We apply an asymmetric version of Kirman's herding model to volatile
financial markets. In the relation between returns and agent concentration we
use the square root law proposed by Zhang. This can be derived by extending the
idea of a critical mean field theory suggested by Plerou et al. We show that
this model is equivalent to the so called 3/2-model of stochastic volatility.
The description of the unconditional distribution for the absolute returns is
in good agreement with the DAX independent whether one uses the square root or
a conventional linear relation. Only the statistic of extreme events prefers
the former. The description of the autocorrelations are in much better
agreement for the square root law. The volatility clusters are described by a
scaling law for the distribution of returns conditional to the value at the
previous day in good agreement with the data.
