Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-29T07:00:25.207Z Has data issue: false hasContentIssue false
  • English
  • Français

PRICE IMPACT OF LARGE ORDERS USING HAWKES PROCESSES

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  06 May 2019

L. R. AMARAL Open the ORCID record for L. R. AMARAL [Opens in a new window]  and
A. PAPANICOLAOU Open the ORCID record for A. PAPANICOLAOU [Opens in a new window]
L. R. AMARAL*
Affiliation:
Department of Finance and Risk Engineering, NYU Tandon School of Engineering, 6 MetroTech Center, Brooklyn, NY 11201, USA email [email protected], [email protected]
A. PAPANICOLAOU
Affiliation:
Department of Finance and Risk Engineering, NYU Tandon School of Engineering, 6 MetroTech Center, Brooklyn, NY 11201, USA email [email protected], [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

price-impact functionlimit order booksexecution of large ordersHawkes processes

MSC classification

Primary: 91B26: Market models (auctions, bargaining, bidding, selling, etc.)
Secondary: 60G55: Point processes 91B70: Stochastic models
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 2 , April 2019 , pp. 161 - 194
Copyright
© 2019 Australian Mathematical Society 

References

Alfonsi, A. and Blanc, P., “Dynamic optimal execution in a mixed-market-impact Hawkes price model”, Finance Stoch. 20 (2016) 183–218; doi:10.1007/s00780-015-0282-y.Google Scholar
Almgren, R. and Chriss, N., “Optimal execution of portfolio transactions”, J. Risk 3 (2001) 5–39; doi:10.21314/JOR.2001.041.Google Scholar
Almgren, R., Thum, C., Hauptmann, E. and Li, H., “Direct estimation of equity market impact”, Risk 18 (2005) 58–62; doi:10.1.1.146.1241.Google Scholar
Avellaneda, M., Algorithmic and high-frequency trading: an overview (Quant Congress, USA, 2011); (Retrieved May 2013);https://www.math.nyu.edu/faculty/avellane/QuantCongressUSA2011AlgoTradingLAST.pdf.Google Scholar
Avellaneda, M. and Stoikov, S., “High-frequency trading in a limit order book”, Quant. Finance 8 (2008) 217–224; doi:10.1080/14697680701381228.Google Scholar
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) 1–12; doi:10.1140/epjb/e2012-21005-8.Google Scholar
Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J. F., “Modelling microstructure noise with mutually exciting point processes”, Quant. Finance 13 (2013) 65–77; doi:10.1080/14697688.2011.647054.Google Scholar
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) 2475–2499; doi:10.1016/j.spa.2013.04.007.Google Scholar
Bacry, E., Mastromatteo, I. and Muzy, J. F., “Hawkes processes in finance”, Market Microstructure and Liquidity 1 (2015) ID:1550005; doi:10.1142/S2382626615500057.Google Scholar
Bacry, E. and Muzy, J. F., “Hawkes model for price and trades high-frequency dynamics”, Quant. Finance 14 (2014) 1147–1166; doi:10.1080/14697688.2014.897000.Google Scholar
Bechler, K. and Ludkovski, M., “Optimal execution with dynamic order flow imbalance”, SIAM J. Financial Math. 6 (2015) 1123–1151; doi:10.1137/140992254.Google Scholar
Bouchaud, J. P., “Price impact”, in: Encyclopedia of quantitative finance (John Wiley and Sons, 2010); doi:10.1002/9780470061602.eqf18006.Google Scholar
Carmona, R. and Webster, K., “High frequency market making”, Preprint, 2012, arXiv:1210.578.Google Scholar
Cartea, A., Jaimungal, S. and Ricci, J., “Buy low, sell high: a high frequency trading perspective”, SIAM J. Financial Math. 5 (2014) 415–444; doi:10.1137/130911196.Google Scholar
Cont, R., “Statistical modeling of high-frequency financial data”, IEEE Signal Process. Mag. 28 (2011) 16–25; doi:10.1109/MSP.2011.941548.Google Scholar
Cont, R., Kukanov, A. and Stoikov, S., “The price impact of order book events”, J. Financial Econ. 12 (2014) 47–88; doi:10.2139/ssrn.1712822.Google Scholar
Da Fonseca, J. and Zaatour, R., “Hawkes process: fast calibration, application to trade clustering, and diffusive limit”, J. Futures Markets 34 (2014) 548–579; doi:10.1002/fut.21644.Google Scholar
Donier, J., Bonart, J., Mastromatteo, I. and Bouchaud, J. P., “A fully consistent, minimal model for non-linear market impact”, Quant. Finance 15 (2015) 1109–1121; doi:10.1080/14697688.2015.1040056.Google Scholar
Gatheral, J., “No-dynamic-arbitrage and market impact”, Quant. Finance 10 (2010) 749–759; doi:10.1080/14697680903373692.Google Scholar
Hawkes, A. G., “Spectra of some self-exciting and mutually exciting point processes”, Biometrika 58 (1971) 83–90; doi:10.2307/2334319.Google Scholar
Haynes, R. and Roberts, J., Automated trading in futures markets, CFTC White Paper (2015); https://www.cftc.gov/sites/default/files/idc/groups/public/@economicanalysis/documents/file/oce_automatedtrading.pdf.Google Scholar
Huberman, G. and Stanzl, W., “Price manipulation and quasi-arbitrage”, Economentrica 72 (2004) 1247–1275; doi:10.1111/j.1468-0262.2004.00531.x.Google Scholar
Karatzas, I. and Shreve, S., Brownian motion and stochastic, calculus, 2nd edn (Springer, New York, 1998).Google Scholar
Kyle, A., “Continuous auctions and insider trading”, Econometrica 53 (1985) 1315–1335; doi:10.2307/1913210.Google Scholar
Laub, P., Taimre, T. and Pollett, P., “Hawkes processes”, Preprint, 2015, arXiv:1507.02822.Google Scholar
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.Google Scholar
Miller, R. S. and Shorter, G., “High frequency trading: overview of recent developments”, Congressional Res. Serv. (2016) 1–15; https://digital.library.unt.edu/ark:/67531/metadc847719/.Google Scholar
Obizhaeva, A. and Wang, J., “Optimal trading strategy and supply/demand dynamics”, J. Finance Markets 16 (2013) 1–32; doi:10.1016/j.finmar.2012.09.001.Google Scholar
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.Google Scholar
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.Google Scholar
Shriyaev, A., Probability, 2nd edn (Springer, New York, 1996).Google Scholar
Rogers, L. C. G. and Singh, S., “The cost of illiquidity and its effects on hedging”, Math. Finance 20 (2010) 597–615; doi:10.1111/j.1467-9965.2010.00413.x.Google Scholar
Smith, E., Farmer, J. D., Gillemot, L. and Krishnamurthy, S., “Statistical theory of the continuous double auction”, Quant. Finance 3 (2003) 481–514; doi:10.1088/1469-7688/3/6/307.Google Scholar
Vacarescu, A., “Filtering and parameter estimation for partially observed generalized Hawkes processes”, Ph.D. Thesis, Stanford University, 2011; https://purl.stanford.edu/tc922qd0500.Google Scholar
Weber, P. and Rosenow, B., “Order book approach to price impact”, Quant. Finance 5 (2005) 357–364; doi:10.1080/14697680500244411.Google Scholar