  We develop a behavioral model for liquidity and volatility based on empirical
regularities in trading order flow in the London Stock Exchange. This can be
viewed as a very simple agent based model in which all components of the model
are validated against real data. Our empirical studies of order flow uncover
several interesting regularities in the way trading orders are placed and
cancelled. The resulting simple model of order flow is used to simulate price
formation under a continuous double auction, and the statistical properties of
the resulting simulated sequence of prices are compared to those of real data.
The model is constructed using one stock (AZN) and tested on 24 other stocks.
For low volatility, small tick size stocks (called Group I) the predictions are
very good, but for stocks outside Group I they are not good. For Group I, the
model predicts the correct magnitude and functional form of the distribution of
the volatility and the bid-ask spread, without adjusting any parameters based
on prices. This suggests that at least for Group I stocks, the volatility and
heavy tails of prices are related to market microstructure effects, and
supports the hypothesis that, at least on short time scales, the large
fluctuations of absolute returns are well described by a power law with an
exponent that varies from stock to stock.
