Statistical properties of stock order books: empirical results and models

We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of incoming limit order prices, which follows a power-law around the current price with a diverging mean; and (ii) the humped shape of the average order book, which can be quantitatively reproduced using a ‘zero intelligence’ numerical model, and qualitatively predicted using a simple approximation. Financial markets offer an amazing source of detailed data on the collective behaviour of interacting agents. It is possible to find many reproducible patterns and even to perform controled experiments, where the response of the price to agiven perturbation is studied. This brings this rather atypical subject into the realm of experimental science. The situation is simple and well defined, since many agents, with all the same goal, trade the very same asset. As such, the statistical analysis of financial markets offers an interesting testing ground for more ambitious theories of human activities. One may wonder to what extent it is necessary to invoke human intelligence or rationality to explain the various universal statistical laws which have been recently unveiled by the systematic analysis of very large data sets.