the price impact of order book events - market orders, limit orders and cancellations

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  a   r    X    i   v   :    0    9    0    4  .    0    9    0    0   v    2    [   q      f    i   n  .    T    R    ]    2    3    M   a   r    2    0    1    0 The price impact of order book even ts: mark et order s, limit orders and cancel lati ons Zolt´ an Eisler, 1 Jean-Philippe Bouchaud, 1 and Julien Kockelkoren 1 1 Capital F und Management, Paris, F ranc e (Dated: March 24, 2010) 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 dierent events, and thei r respe ctiv e impac t on future price changes . We dene and extract from the data the “bare” impa ct these even ts 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-uctuating is in good agreement wit h the data. For small tick stocks, however, bare impact s must contain a histo ry dependent part, reecting the inter nal uctuations of the order b ook. We show that this eect can be accurately desc ribed by an autoregr essi ve model on the past order ow . This framew ork allows us to decompose the impac t of an eve nt into three parts: an instant aneou s jump compone nt, the modication of the future rates of the dierent events, and the modication of the jump sizes of futu re events. We compare in detail the pres ent formal ism with the temporar y impac t 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. Keyw ords: price impact, market orders, limit orders, canc ellations, marke t micros tructure, order ow Contents 1. Int roduction 2 2. Impact of mar ke t orders: a short revie w 3 2.1. The transient impact model 3 2.2. History dependence of the impact function 4 2.3. The role of hidden events 5 2.4. Relation with Hasbrouc k’s VAR model 5 3. Data and notations 6 4. Correlation and response functions 7 4.1. The autocorrelation of ǫ and s 7 4.2. The signed event-event correlation functions 8 4.3. The unsigned event-event correlation functions 10 4.4. The response function 11 5. The temporary impact model 11 6. A constant impact model 13 7. The gap dynamics of small tick stocks 16 7.1. A linear model for gap uctuations 16 7.2. A linear model for gap uctuations 17 7.3. The nal model for small ticks 18 7.4. Interpretation: direct impact vs. induced impact 20 8. Conclusi ons 22 References 23 A. The dependence of the spread on the event ow 23 B. Plots of various correlat ion functions 26

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Page 1: The Price Impact of Order Book Events - Market Orders, Limit Orders and Cancellations

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