The price impact of order book events: market orders, limit orders and cancellations

TL;DR

This paper empirically analyzes how market orders, limit orders, and cancellations influence future price changes, revealing different impact dynamics for large and small tick stocks and proposing a comprehensive impact model.

Contribution

It introduces a detailed empirical framework for decomposing and modeling the impact of various order book events on prices, including a history-dependent impact for small tick stocks.

Findings

For large tick stocks, a permanent impact model fits well.

For small tick stocks, impact depends on order flow history.

The model extends to bid-ask spread dynamics.

Abstract

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the "bare" impact these events would have, if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model on the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the future gaps behind the best quotes. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid-ask spread.