Skip to main content Accessibility help


  • L. R. AMARAL (a1) and A. PAPANICOLAOU (a1)


We introduce a model for the execution of large market orders in limit order books, and use a linear combination of self-exciting Hawkes processes to model asset-price dynamics, with the addition of a price-impact function that is concave in the order size. A criterion for a general price-impact function is introduced, which is used to show how specification of a concave impact function affects order execution. Using our model, we examine the immediate and permanent impacts of large orders, analyse the potential for price manipulation, and show the effectiveness of the time-weighted average price strategy. Our model shows that price depends on the balance between the intensities of the Hawkes process, which can be interpreted as a dependence on order-flow imbalance.


Corresponding author


Hide All
[1] Alfonsi, A. and Blanc, P., “Dynamic optimal execution in a mixed-market-impact Hawkes price model”, Finance Stoch. 20 (2016) 183218; doi:10.1007/s00780-015-0282-y.
[2] Almgren, R. and Chriss, N., “Optimal execution of portfolio transactions”, J. Risk 3 (2001) 539; doi:10.21314/JOR.2001.041.
[3] Almgren, R., Thum, C., Hauptmann, E. and Li, H., “Direct estimation of equity market impact”, Risk 18 (2005) 5862; doi:
[4] Avellaneda, M., Algorithmic and high-frequency trading: an overview (Quant Congress, USA, 2011); (Retrieved May 2013);
[5] Avellaneda, M. and Stoikov, S., “High-frequency trading in a limit order book”, Quant. Finance 8 (2008) 217224; doi:10.1080/14697680701381228.
[6] Bacry, E., Dayri, K. and Muzy, J. F., “Non-parametric kernel estimation for symmetric Hawkes processes application to high frequency financial data”, Eur. Phys. J. B 85 (2012) 112; doi:10.1140/epjb/e2012-21005-8.
[7] Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J. F., “Modelling microstructure noise with mutually exciting point processes”, Quant. Finance 13 (2013) 6577; doi:10.1080/14697688.2011.647054.
[8] Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J. F., “Some limit theorems for Hawkes processes and application to financial statistics”, Stochastic Process. Appl. 123 (2013) 24752499; doi:10.1016/
[9] Bacry, E., Mastromatteo, I. and Muzy, J. F., “Hawkes processes in finance”, Market Microstructure and Liquidity 1 (2015) ID:1550005; doi:10.1142/S2382626615500057.
[10] Bacry, E. and Muzy, J. F., “Hawkes model for price and trades high-frequency dynamics”, Quant. Finance 14 (2014) 11471166; doi:10.1080/14697688.2014.897000.
[11] Bechler, K. and Ludkovski, M., “Optimal execution with dynamic order flow imbalance”, SIAM J. Financial Math. 6 (2015) 11231151; doi:10.1137/140992254.
[12] Bouchaud, J. P., “Price impact”, in: Encyclopedia of quantitative finance (John Wiley and Sons, 2010); doi:10.1002/9780470061602.eqf18006.
[13] Carmona, R. and Webster, K., “High frequency market making”, Preprint, 2012, arXiv:1210.578.
[14] Cartea, A., Jaimungal, S. and Ricci, J., “Buy low, sell high: a high frequency trading perspective”, SIAM J. Financial Math. 5 (2014) 415444; doi:10.1137/130911196.
[15] Cont, R., “Statistical modeling of high-frequency financial data”, IEEE Signal Process. Mag. 28 (2011) 1625; doi:10.1109/MSP.2011.941548.
[16] Cont, R., Kukanov, A. and Stoikov, S., “The price impact of order book events”, J. Financial Econ. 12 (2014) 4788; doi:10.2139/ssrn.1712822.
[17] Da Fonseca, J. and Zaatour, R., “Hawkes process: fast calibration, application to trade clustering, and diffusive limit”, J. Futures Markets 34 (2014) 548579; doi:10.1002/fut.21644.
[18] Donier, J., Bonart, J., Mastromatteo, I. and Bouchaud, J. P., “A fully consistent, minimal model for non-linear market impact”, Quant. Finance 15 (2015) 11091121; doi:10.1080/14697688.2015.1040056.
[19] Gatheral, J., “No-dynamic-arbitrage and market impact”, Quant. Finance 10 (2010) 749759; doi:10.1080/14697680903373692.
[20] Hawkes, A. G., “Spectra of some self-exciting and mutually exciting point processes”, Biometrika 58 (1971) 8390; doi:10.2307/2334319.
[21] Haynes, R. and Roberts, J., Automated trading in futures markets, CFTC White Paper (2015);
[22] Huberman, G. and Stanzl, W., “Price manipulation and quasi-arbitrage”, Economentrica 72 (2004) 12471275; doi:10.1111/j.1468-0262.2004.00531.x.
[23] Karatzas, I. and Shreve, S., Brownian motion and stochastic, calculus, 2nd edn (Springer, New York, 1998).
[24] Kyle, A., “Continuous auctions and insider trading”, Econometrica 53 (1985) 13151335; doi:10.2307/1913210.
[25] Laub, P., Taimre, T. and Pollett, P., “Hawkes processes”, Preprint, 2015, arXiv:1507.02822.
[26] Mastromatteo, I., “Apparent impact: the hidden cost of one-shot trades”, J. Stat. Mech. Theory Exp. 6 (2015) ID: P06022; doi:10.1088/1742-5468/2015/06/P06022.
[27] Miller, R. S. and Shorter, G., “High frequency trading: overview of recent developments”, Congressional Res. Serv. (2016) 115;
[28] Obizhaeva, A. and Wang, J., “Optimal trading strategy and supply/demand dynamics”, J. Finance Markets 16 (2013) 132; doi:10.1016/j.finmar.2012.09.001.
[29] Plerou, V., Gopikrishnan, P., Gabaix, X. and Stanley, H. E., “Quantifying stock-price response to demand fluctuations”, Phys. Rev. E 66 (2002) ID: 027104; doi:10.1103/PhysRevE.66.027104.
[30] Pohl, M., Ristig, A., Schachermayer, W. and Tangpi, L., “The amazing power of dimensional analysis: quantifying market impact”, Market Microstructure and Liquidity 3 (2017) ID: 1850004; doi:10.1142/S2382626618500041.
[31] Shriyaev, A., Probability, 2nd edn (Springer, New York, 1996).
[32] Rogers, L. C. G. and Singh, S., “The cost of illiquidity and its effects on hedging”, Math. Finance 20 (2010) 597615; doi:10.1111/j.1467-9965.2010.00413.x.
[33] Smith, E., Farmer, J. D., Gillemot, L. and Krishnamurthy, S., “Statistical theory of the continuous double auction”, Quant. Finance 3 (2003) 481514; doi:10.1088/1469-7688/3/6/307.
[34] Vacarescu, A., “Filtering and parameter estimation for partially observed generalized Hawkes processes”, Ph.D. Thesis, Stanford University, 2011;
[35] Weber, P. and Rosenow, B., “Order book approach to price impact”, Quant. Finance 5 (2005) 357364; doi:10.1080/14697680500244411.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed