Deep Limit Order Book Events Dynamics

This paper analyzes the limit order book events arrival dependency structure using high-dimensional Hawkes processes. We seek for recurrent relationships among events from a set of 86 event types which in addition to transactions, includes limit order submissions and cancellations taking place up to the 20th depth level of the order book. We focus on BMW, SAP, and ADS, three liquid DAX 30 index stocks for which we have a microsecond stamped high-frequency dataset covering the 61 trading day period going from February 1 to March 31, 2013. For each stock, we build a tailored descriptive model by selecting recurrent events relationships. Estimated on a daily basis, we find that the selected models offer interesting data fitting performance, particularly for limit order submissions and cancellations occurring on the first five price levels of the order book. Finally, we use the comprehensive sets of estimated parameters to describe a global events arrival dynamics that we relate to the potential behaviors of market participants having different objectives and directional views.