  Statistical properties of an order book and the effect they have on price
dynamics were studied using the high-frequency NASDAQ Level II data. It was
observed that the size distribution of marketable orders (transaction sizes)
has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The
distribution of limit order sizes was found to be consistent with a power law
with an exponent close to 2. A somewhat better fit to this distribution was
obtained by using a log-normal distribution with an effective power law
exponent equal to 2 in the middle of the observed range. The depth of the order
book measured as a price impact of a hypothetical large market order was
observed to be a non-linear function of its size. A large imbalance in the
number of limit orders placed at bid and ask sides of the book was shown to
lead to a short term deterministic price change, which is in accord with the
law of supply and demand.
