Modeling aggressive market order placements with Hawkes factor models

Autoři: Hai-Chuan Xu aff001;  Wei-Xing Zhou aff001
Působiště autorů: Research Center for Econophysics, East Chine University of Science and Technology, Shanghai, China aff001;  Department of Finance, East Chine University of Science and Technology, Shanghai, China aff002;  Department of Mathematics, East China University of Science and Technology, Shanghai, China aff003
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article


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.

Klíčová slova:

Finance – Microstructure – Stock markets – Fluid flow – Kernel functions – Exponential functions – Operator theory – Commodity markets


1. Hawkes AG. Point spectra of some mutually exciting point processes. J R Stat Soc B. 1971;33(3):438–443.

2. Hawkes AG. Spectra of some self-exciting and mutually exciting point processes. Biometrika. 1971;58(1):83–90. doi: 10.1093/biomet/58.1.83

3. Bacry E, Mastromatteo I, Muzy JF. Hawkes Processes in Finance. Market Microstructure and Liquidity. 2015;1(59).

4. Hawkes AG. Hawkes processes and their applications to finance: A review. Quant Financ. 2018;18(2):193–198. doi: 10.1080/14697688.2017.1403131

5. Large J. Measuring the resiliency of an electronic limit order book. J Financ Markets. 2007;10:1–25. doi: 10.1016/j.finmar.2006.09.001

6. Filimonov V, Sornette D. Quantifying reflexivity in financial markets: Toward a prediction of flash crashes. Phys Rev E. 2012;85(5):056108. doi: 10.1103/PhysRevE.85.056108

7. Lallouache M, Challet D. The limits of statistical significance of Hawkes processes fitted to financial data. Quant Financ. 2016;16(1):1–11. doi: 10.1080/14697688.2015.1068442

8. Bormetti G, Calcagnile LM, Treccani M, Corsi F, Marmi S, Lillo F. Modelling systemic price cojumps with Hawkes factor models. Quant Financ. 2015;15(7):1137–1156. doi: 10.1080/14697688.2014.996586

9. Hardiman SJ, Bercot N, Bouchaud JP. Critical reflexivity in financial markets: A Hawkes process analysis. Eur Phys J B. 2013;86(10):442. doi: 10.1140/epjb/e2013-40107-3

10. Saichev A, Sornette D. Superlinear scaling of offspring at criticality in branching processes. Phys Rev E. 2014;89(1):012104. doi: 10.1103/PhysRevE.89.012104

11. Filimonov V, Sornette D. Apparent criticality and calibration issues in the Hawkes self-excited point process model: Application to high-frequency financial data. Quant Financ. 2015;15(8):1293–1314. doi: 10.1080/14697688.2015.1032544

12. Filimonov V, Bicchetti D, Maystre N, Sornette D. Quantification of the high level of endogeneity and of structural regime shifts in commodity markets. J Int Money Financ. 2014;42:174–192. doi: 10.1016/j.jimonfin.2013.08.010

13. Filimonov V, Wheatley S, Sornette D. Effective measure of endogeneity for the Autoregressive Conditional Duration point processes via mapping to the self-excited Hawkes process. Commun Nonlinear Sci Numer Simul. 2015;22(1):23–37. doi: 10.1016/j.cnsns.2014.08.042

14. Chavez-Demoulin V, Mcgill JA. High-frequency financial data modeling using Hawkes processes. J Bank Financ. 2012;36(12):3415–3426. doi: 10.1016/j.jbankfin.2012.08.011

15. Blanc P, Donier J, Bouchaud JP. Quadratic Hawkes processes for financial prices. Quant Financ. 2017;17(2):171–188. doi: 10.1080/14697688.2016.1193215

16. Bowsher CG. Modelling security markets in continuous time: Intensity based, multivariate point process models. J Econometrics. 2007;141(2):876–912. doi: 10.1016/j.jeconom.2006.11.007

17. Rambaldi M, Bacry E, Lillo F. The role of volume in order book dynamics: A multivariate Hawkes process analysis. Quant Financ. 2017;17(7):999–1020. doi: 10.1080/14697688.2016.1260759

18. Muni Toke I, Pomponio F. Modelling trades-through in a limited order book using Hawkes processes. Economics: The Open-Access, Open-Assessment E-Journal. 2012;6(2012-22):1–23.

19. Bacry E, Muzy JF. Hawkes model for price and trades high-frequency dynamics. Quant Financ. 2014;14(7):1147–1166. doi: 10.1080/14697688.2014.897000

20. Zheng B, Roueff F, Abergel F. Modelling bid and ask prices using constrained Hawkes processes: Ergodicity and scaling limit. SIAM J Financial Math. 2014;5(1):99–136. doi: 10.1137/130912980

21. Calcagnile LM, Bormetti G, Treccani M, Marmi S, Lillo F. Collective synchronization and high frequency systemic instabilities in financial markets. Quant Financ. 2018;18(2):237–247. doi: 10.1080/14697688.2017.1403141

22. Rambaldi M, Pennesi P, Lillo F. Modeling foreign exchange market activity around macroeconomic news: Hawkes-process approach. Phys Rev E. 2015;91(1):012819. doi: 10.1103/PhysRevE.91.012819

23. Aït-Sahalia Y, Cacho-Diaz J, Laeven RJA. Modeling financial contagion using mutually exciting jump processes. J Financ Econ. 2015;117(3):585–606. doi: 10.1016/j.jfineco.2015.03.002

24. Lu X, Abergel F. High-dimensional Hawkes processes for limit order books: Modelling, empirical analysis and numerical calibration. Quant Financ. 2018;(2):249–264. doi: 10.1080/14697688.2017.1403142

25. Bacry E, Jaisson T, Muzy JC. Estimation of slowly decreasing Hawkes kernels: Application to high-frequency order book dynamics. Quant Financ. 2016;16(8):1179–1201. doi: 10.1080/14697688.2015.1123287

26. Jiang ZQ, Chen W, Zhou WX. Scaling in the distribution of intertrade durations of Chinese stocks. Physica A. 2008;387:5818–5825. doi: 10.1016/j.physa.2008.06.039

27. Jiang ZQ, Chen W, Zhou WX. Detrended fluctuation analysis of intertrade durations. Physica A. 2009;388(4):433–440. doi: 10.1016/j.physa.2008.10.028

28. Ruan YP, Zhou WX. Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant. Physica A. 2011;390(9):1646–1654. doi: 10.1016/j.physa.2011.01.001

29. Engle RF, Russell JR. Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica. 1998;66(5):1127–1162. doi: 10.2307/2999632

30. Brémaud P, Massoulié L. Stability of nonlinear Hawkes processes. Atmos Pollut Res. 1996;24(3):1563–1588.

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