Abstract
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 a Shenzhen Stock Exchange 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.
Highlights
Self-exciting and mutually exciting point processes are a natural extension of Poisson processes, which are first proposed by Alan G
We find that the exponential kernel with a smooth cut-off at short times produces better calibration than the monotonous exponential kernel does
The kernel function used here is the smooth cut-off biexponential function given in Eq (2)
Summary
Self-exciting and mutually exciting point processes are a natural extension of Poisson processes, which are first proposed by Alan G. Hawkes processes have been applied to characterize clustering events in finance, to high-frequency data and market microstructure [3, 4], because many types of events are clustered in time such as order submissions [5], mid-quotes changes [6], transactions [7] and extreme returns occurrences [8]. Through calibrating the self-exciting Hawkes model on time series of price changes, the endogeneity and structural regime shifts are quantified in commodity markets [12]. The branching ratio can serve as an effective measure of endogeneity for the autoregressive conditional duration point processes [13]. The Hawkes models are further extended to quadratic by allowing all feedback effects in the jump intensity that are linear and quadratic in past returns [15]
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