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)].