Mathematical Finance Seminar

March 6, 2003 , 5:30 PM to 7:00 PM

Marc Potters, Science & Finance, Capital Fund Management

Statistical properties of order books and price impact

We present some new statistical properties of order books. We analyze data from the Island ECN and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time of a limit order as a function of the distance from the best price. The data will be compared to the prediction of a `zero intelligence' model which we analyze numerically and solve using a simple approximation. We also determine the `price impact' function using French and British stocks, and find a logarithmic, rather than a power-law, dependence of the price response on the volume. The weak time dependence of the response function shows that the impact is, surprisingly, quasi-permanent, and suggests that trading itself is interpreted by the market as new information. [work in collaboration with J-P Bouchaud (CEA-Saclay, S&F/CFM)].