We propose that the minimal requirements for a model of stock market price
fluctuations should comprise time asymmetry, robustness with respect to
connectivity between agents, ``bounded rationality'' and a probabilistic
description. We also compare extensively two previously proposed models of
log-periodic behavior of the stock market index prior to a large crash. We find
that the model which follows the above requirements outperforms the other with
a high statistical significance.Comment: 18 pages with 4 figures. Submitted to Eur.Phys.
