Modelling bid and ask prices using constrained Hawkes processes: Ergodicity and scaling limit

SIAM Journal on Financial Mathematics

Volumn 5, Issue 1, 2014, Pages 99-136

  Zheng, Ban ^a   Roueff, François ^a   Abergel, Frédéric ^b  

^a INSTITUT TELECOM   (France)

^b Ecole Centrale de Paris   (France)

Author keywords

Bid ask spread; Ergodicity; Hawkes processes; Limit order book; Markov model; Microstructure noise; Point processes; Scaling limit

Indexed keywords

EID: 84920866642     PISSN: None     EISSN: 1945497X     Source Type: Journal    
DOI: 10.1137/130912980     Document Type: Article

References (36)

1. F. ABERGEL AND A. JEDIDI, A mathematical approach to order book modeling, Int. J. Theor. Appl. Finance, 16 (2013), 1350025.
2. Y. AÏT-SAHALIA, J. CACHO-DIAZ, AND R. J. A. LAEVEN, Modeling Financial Contagion Using Mutually Exciting Jump Processes, Working Paper 15850, National Bureau of Economic Research, Cambridge, MA, 2010.
3. S. ASMUSSEN, Applied Probability and Queues, 2nd ed., Appl. Math. (N. Y.) 51, Springer-Verlag, New York, 2003.
4. E. BACRY, K. DAYRI, AND J. F. MUZY, Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data, Eur. Phys. J. B, 85 (2012), pp. 1-12.
5. E. BACRY, S. DELATTRE, M. HOFFMANN, AND J. F. MUZY, Modelling microstructure noise with mutually exciting point processes, Quant. Finance, 13 (2013), pp. 65-77.
6. E. BACRY, S. DELATTRE, M. HOFFMANN, AND J. F. MUZY, Scaling Limits for Hawkes Processes and Application to Financial Statistics, preprint, 2012.
7. L. BAUWENS AND N. HAUTSCH, Dynamic Latent Factor Models for Intensity Processes, CORE Discussion Papers 2003103, Center for Operations Research and Econometrics (CORE), Université catholique de Louvain, Louvain-La-Neuve, Belgium, 2003.
8. L. BAUWENS AND N. HAUTSCH, Modelling financial high frequency data using point processes, in Handbook of Financial Time Series, Springer, Berlin, Heidelberg, 2009, pp. 953-979.
9. B. BIAIS, P. HILLION, AND C. SPATT, An empirical analysis of the limit order book and the order flow in the Paris Bourse, J. Finance, 50 (1995), pp. 1655-1689.
10. J. P. BOUCHAUD, J. D. FARMER, AND F. LILLO, How markets slowly digest changes in supply and demand, in Handbook of Financial Markets: Dynamics and Evolution, Elsevier, Amsterdam, 2009, pp. 57-160.
11. C. BOWSHER, Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models, Nuffield College Economics Discussion Papers, Nuffield College, Oxford, UK, 2002.
12. C. BOWSHER, Modelling security market events in continuous time: Intensity based, multivariate point process models, J. Econometrics, 141 (2007), pp. 876-912.
13. P. BRÉMAUD AND L. MASSOULIÉ, Stability of nonlinear Hawkes processes, Ann. Probab., 24 (1996), pp. 1563-1588.
14. A. CHAKRABORTI, I. MUNI TOKE, M. PATRIARCA, AND F. ABERGEL, Econophysics review: I. Empirical facts, Quant. Finance, 11 (2011), pp. 991-1012.
15. A. CHAKRABORTI, I. MUNI TOKE, M. PATRIARCA, AND F. ABERGEL, Econophysics review: II. Agentbased models, Quant. Finance, 11 (2011), pp. 1013-1041.
16. R. CONT AND A. DE LARRARD, Price dynamics in a Markovian limit order market, SIAM J. Financial Math., 4 (2013), pp. 1-25.
17. R. CONT, S. STOIKOV, AND R. TALREJA, A stochastic model for order book dynamics, Oper. Res., 58 (2010), pp. 549-563.
18. D. J. DALEY AND D. VERE-JONES, An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods, 2nd ed., Probab. Appl. (N. Y.), Springer-Verlag, New York, 2003.
19. P. EMBRECHTS, T. LINIGER, AND L. LIN, Multivariate Hawkes processes: An application to financial data, J. Appl. Probab., 48A (2011), pp. 367-378.
20. E. ERRAIS, K. GIESECKE, AND L. R. GOLDBERG, Affine point processes and portfolio credit risk, SIAM J. Financial Math., 1 (2010), pp. 642-665.
21. J. D. FARMER, L. GILLEMOT, F. LILLO, S. MIKE, AND A. SEN, What really causes large price changes?, Quant. Finance, 4 (2004), pp. 383-397.
22. T. FLETCHER, Z. HUSSAIN, AND J. SHAWE-TAYLOR, Multiple kernel learning on the limit order book, J. Machine Learn. Res.-Proc. Track, 11 (2010), pp. 167-174.
23. C. GOURIEROUX, J. JASIAK, AND G. LE FOL, Intra-day market activity, J. Financ. Market, 2 (1999), pp. 193-226.
24. P. HEWLETT, Clustering of order arrivals, price impact and trade path optimisation, in Workshop on Financial Modeling with Jump Processes, 2006.
25. B. HOLLIFIELD, R. A. MILLER, AND P. SANDAS, Empirical analysis of limit order markets, Rev. Econom. Stud., 71 (2004), pp. 1027-1063.
26. J. H. LARGE, Measuring the resiliency of an electronic limit order book, J. Financ. Market, 10 (2007), pp. 1-25.
27. T. F. LINIGER, Multivariate Hawkes Processes, Ph.D. thesis, ETH Zürich, Zürich, Switzerland, 2009.
28. S. MEYN AND R. L. TWEEDIE, Markov Chains and Stochastic Stability, 2nd ed., Cambridge University Press, Cambridge, UK, 2009.
29. I. MUNI TOKE AND F. POMPONIO, Modelling trades-through in a limit order book using Hawkes processes, Economics: The Open-Access, Open-Assessment E-Journal, 6 (2012), pp. 1-23.
30. D. OAKES, The Markovian self-exciting process, J. Appl. Probability, 12 (1975), pp. 69-77.
31. C. A. PARLOUR, Price dynamics in limit order markets, Rev. Financ. Stud., 11 (1998), pp. 789-816.
32. I. ROCU, A dynamic model of the limit order book, Rev. Financ. Stud., 22 (2009), pp. 4601-4641.
33. E. SMITH, J. D. FARMER, L. GILLEMOT, AND S. KRISHNAMURTHY, Statistical theory of the continuous double auction, Quant. Finance, 3 (2003), pp. 481-514.
34. W. WHITT, Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues, Springer Ser. Oper. Res., Springer-Verlag, New York, 2002.
35. B. ZHENG, Détection d'événements rares dans les données hautes fréquences et applications au trading algorithmique, Ph.D. thesis, Télécom ParisTech, Paris, France, to appear.
36. B. ZHENG, E. MOULINES, AND F. ABERGEL, Price jump prediction in a limit order book, J. Math. Finance, 3 (2013), pp. 242-255.