Hawkes model specification for limit order books

This paper discusses Hawkes modeling of order arrivals in limit order books. We model the flow of market orders, limit orders, and cancelations by a self- and crossexciting multitype marked Hawkes process with state-dependent baseline intensities. The marks carry the order sizes and the state of the book is summarized by the ‘limit-order-book imbalance’. We specify the model very carefully – with few a priori assumptions: we select the non-zero excitements (the ‘Hawkes skeleton’), the shape of the decay kernels, and the shape of the impact functions in a nonparametric manner. Furthermore, we show that our data exhibit perfect bid–ask symmetry. We observe that the imbalance of the order book explains the probability for a bid (ask) market order – given the occurrence of a market order – in a perfectly linear manner. Thus, we include a term involving the imbalance in the baseline intensity of the process. We calibrate the specified parametric model by maximum likelihood estimation and discuss the results. Finally, we apply the fitted model in order to estimate the conditional distribution of the next order type. This opens the door to order-type prediction.