Price fluctuations from the order book perspective - empirical facts and a simple model

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.