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

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 of 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 jump sizes of future events. 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.

Keywords:

• Market microstructure
• Markov processes
• Limit orders
• Price formation

Notes

† In the following, we only focus on price changes over short periods of time, so that the following additive model is adequate. For longer time scales, one should worry about multiplicative effects, which in this formalism would naturally arise from the fact that the bid–ask spread, and the gaps in the order book, are a fraction of the price. Therefore, the impact itself, 𝒢, is expected to be proportional to a moving average of the price. See Bouchaud and Potters (2000) for a discussion of this point.

† The results for these markets are not reproduced here for lack of space, but the corresponding data are available upon request.

‡ To identify multiple trades that are initiated by the same market order, we consider as one market order all the trades in a given stock that occur on the same side of the book within a millisecond. Such a time resolution is sufficient for distinguishing trades initiated by different parties even at times of very intense trading activity.

† Our data also included a small number (≈0.3%) of marketable (or crossing) limit orders. In principle, these could have been treated as a market order (and a consequent limit order for the remaining volume if there was any). Due to technical limitations we decided instead to remove these events and the related price changes.

† There is some sign of oscillations for small tick stocks.

† Note that, in making these plots, we have neglected the first 30 and last 40 minutes of trading days, so they slightly differ from those in section 6. The results of the constant gap model are essentially unchanged regardless of such an exclusion.