Simulation of Stock Price Dynamics by Statistical Order Order-Book Model with Bid Bid-Ask Spread Effect

Abstract

We constructed a basic order order-book model which is based on the Maslov model and includes some empirical results such as distributions of order volume. Although this basic model successfully reproduces power law distributions of price changes, the market price greatly oscillates and the Hurst exponent, which indicates randomness of price fluctuation, of this model is much smaller than that of real data. In order to resolve this problem, we revised the basic order order-book model by adding the effect that the selection probability of order types (i.e. market order, limit orde r and cancel) depends on the bid bid-ask spread. Our revised model still reproduces power law distributions of price changes and the Hurst exponent is improved.