  Price changes are induced by aggressive market orders in stock market. We
introduce a bivariate marked Hawkes process to model aggressive market order
arrivals at the microstructural level. The order arrival intensity is marked by
an exogenous part and two endogenous processes reflecting the self-excitation
and cross-excitation respectively. We calibrate the model for an SSE stock. We
find that the exponential kernel with a smooth cut-off (i.e. the subtraction of
two exponentials) produces much better calibration than the monotonous
exponential kernel (i.e. the sum of two exponentials). The exogenous baseline
intensity explains the $U$-shaped intraday pattern. Our empirical results show
that the endogenous submission clustering is mainly caused by self-excitation
rather than cross-excitation.
