More statistical properties of order books and price impact

TL;DR

This paper explores new statistical properties of order books, analyzing data from Nasdaq to understand order dynamics, shape, and price impact, revealing a logarithmic response and quasi-permanent impact characteristics.

Contribution

It introduces new statistical insights into order book properties and demonstrates a logarithmic price impact function, challenging previous power-law assumptions.

Findings

Price impact follows a logarithmic dependence on volume.

Order book shape and order lifetime vary with distance from best price.

Impact is quasi-permanent, indicating market interpretation of trading as new information.

Abstract

We investigate present some new statistical properties of order books. We analyse data from the Nasdaq 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. 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.