  In this study, we present a simple stochastic order-book model for investors'
swarm behaviors seen in the continuous double auction mechanism, which is
employed by major global exchanges. Our study shows a characteristic called
"fat tail" is seen in the data obtained from our model that incorporates the
investors' swarm behaviors. Our model captures two swarm behaviors: one is
investors' behavior to follow a trend in the historical price movement, and
another is investors' behavior to send orders that contradict a trend in the
historical price movement. In order to capture the features of influence by the
swarm behaviors, from price data derived from our simulations using these
models, we analyzed the price movement range, that is, how much the price is
moved when it is continuously moved in a single direction. Depending on the
type of swarm behavior, we saw a difference in the cumulative frequency
distribution of this price movement range. In particular, for the model of
investors who followed a trend in the historical price movement, we saw the
power law in the tail of the cumulative frequency distribution of this price
movement range. In addition, we analyzed the shape of the tail of the
cumulative frequency distribution. The result demonstrated that one of the
reasons the trend following of price occurs is that orders temporarily swarm on
the order book in accordance with past price trends.
