Studies of the limit order book around large price changes

TL;DR

This paper investigates how the limit order book of liquid stocks relaxes after large intra-day price changes, revealing slow power-law dynamics and suggesting that these may not be driven by strategic agent behavior.

Contribution

It introduces a zero intelligence deposition model that qualitatively reproduces the empirical slow relaxation phenomena observed after large price changes.

Findings

Relaxation of microscopical measures follows a power law with exponent ~0.4.

Empirical and model exponents differ, indicating strategic behavior influences.

Slow relaxations may be explained without strategic agent interactions.

Abstract

We study the dynamics of the limit order book of liquid stocks after experiencing large intra-day price changes. In the data we find large variations in several microscopical measures, e.g., the volatility the bid-ask spread, the bid-ask imbalance, the number of queuing limit orders, the activity (number and volume) of limit orders placed and canceled, etc. The relaxation of the quantities is generally very slow that can be described by a power law of exponent $\approx0.4$. We introduce a numerical model in order to understand the empirical results better. We find that with a zero intelligence deposition model of the order flow the empirical results can be reproduced qualitatively. This suggests that the slow relaxations might not be results of agents' strategic behaviour. Studying the difference between the exponents found empirically and numerically helps us to better identify the role of strategic behaviour in the phenomena.