Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Finance and Stochastics
Published in: Finance and Stochastics 1/2016

01-01-2016

Dynamic optimal execution in a mixed-market-impact Hawkes price model

Authors: Aurélien Alfonsi, Pierre Blanc

Published in: Finance and Stochastics | Issue 1/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We study a linear price impact model, including other liquidity takers, whose flow of orders is driven by a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-form optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust price manipulation strategies in the sense of Huberman and Stanzl (Econometrica, 72:1247–1275, 2004). Instead, a particular set of conditions on the Hawkes model balances the self-excitation of the order flow with the resilience of the price, excludes price manipulation strategies, and gives some market stability.
previous article Superreplication when trading at market indifference prices
next article Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
1.
Abergel, F., Jedidi, A.: A mathematical approach to order book modeling. Int. J. Theor. Appl. Finance 16, 1350025 (2013) MathSciNetCrossRef
2.
Alfonsi, A., Fruth, A., Schied, A.: Optimal execution strategies in limit order books with general shape functions. Quant. Finance 10, 143–157 (2010) MATHMathSciNetCrossRef
3.
Alfonsi, A., Schied, A.: Capacitary measures for completely monotone kernels via singular control. SIAM J. Control Optim. 51, 1758–1780 (2013) MATHMathSciNetCrossRef
4.
Alfonsi, A., Schied, A., Slynko, A.: Order book resilience, price manipulation, and the positive portfolio problem. SIAM J. Financ. Math. 3, 511–533 (2012) MATHMathSciNetCrossRef
5.
Almgren, R., Chriss, N.: Optimal execution of portfolio transactions. J. Risk 3, 5–39 (2000)
6.
Bacry, E., Delattre, S., Hoffmann, M., Muzy, J.F.: Modelling microstructure noise with mutually exciting point processes. Quant. Finance 13, 65–77 (2013) MATHMathSciNetCrossRef
7.
Bacry, E., Delattre, S., Hoffmann, M., Muzy, J.F.: Some limit theorems for Hawkes processes and application to financial statistics. Stoch. Process. Appl. 123, 2475–2499 (2013) MATHMathSciNetCrossRef
8.
9.
Bayraktar, E., Ludkovski, M.: Optimal trade execution in illiquid markets. Math. Finance 21, 681–701 (2011) MATHMathSciNet
10.
Bertsimas, D., Lo, A.: Optimal control of execution costs. J. Financ. Mark. 1, 1–50 (1998) CrossRef
11.
Bouchaud, J.-P., Gefen, Y., Potters, M., Wyart, M.: Fluctuations and response in financial markets: the subtle nature of “random” price changes. Quant. Finance 4, 176–190 (2004) CrossRef
12.
Cont, R., de Larrard, A.: Price dynamics in a Markovian limit order market. SIAM J. Financ. Math. 4, 1–25 (2013) MATHCrossRef
13.
Da Fonseca, J., Zaatour, R.: Hawkes process: fast calibration, application to trade clustering, and diffusive limit. J. Futures Mark. 34, 548–579 (2014)
14.
Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Vol. I. Elementary Theory and Methods, 2nd edn. Probability and Its Applications (New York). Springer, New York (2003) MATH
15.
16.
Eisler, Z., Bouchaud, J.-P., Kockelkoren, J.: The price impact of order book events: market orders, limit orders and cancellations. Quant. Finance 12, 1395–1419 (2012) MATHMathSciNetCrossRef
17.
Embrechts, P., Liniger, T., Lin, L.: Multivariate Hawkes processes: an application to financial data. J. Appl. Probab. 48A(New Frontiers in Applied Probability: a Festschrift for Søren Asmussen), 367–378 (2011) MATHMathSciNetCrossRef
18.
19.
Filimonov, V., Sornette, D.: Quantifying reflexivity in financial markets: toward a prediction of flash crashes. Phys. Rev. E 85, 056108 (2012) CrossRef
20.
Garèche, A., Disdier, G., Kockelkoren, J., Bouchaud, J.-P.: Fokker–Planck description for the queue dynamics of large tick stocks. Phys. Rev. E 88, 032809 (2013) CrossRef
21.
22.
Gatheral, J., Schied, A., Slynko, A.: Transient linear price impact and Fredholm integral equations. Math. Finance 22, 445–474 (2012) MATHMathSciNetCrossRef
23.
Guéant, O.: Optimal execution and block trade pricing: a general framework. Appl. Math. Finance 22, 336–365 (2015) MathSciNetCrossRef
24.
Hardiman, S., Bercot, N., Bouchaud, J.-P.: Critical reflexivity in financial markets: a Hawkes process analysis. Eur. Phys. J. B 86(10), 1–9 (2013) MathSciNetCrossRef
25.
26.
Huang, W., Lehalle, C.-A., Rosenbaum, M.: Simulating and analyzing order book data: the queue-reactive model. J. Am. Stat. Assoc. 110, 107–122 (2015) MathSciNetCrossRef
27.
28.
Thibault, J., Rosenbaum, M.: Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab. 25, 600–631 (2015) MathSciNetCrossRef
29.
Mastromatteo, I., Tóth, B., Bouchaud, J.-P.: Agent-based models for latent liquidity and concave price impact. Phys. Rev. E 89, 042805 (2014) CrossRef
30.
Obizhaeva, A., Wang, J.: Optimal trading strategy and supply/demand dynamics. J. Financ. Mark. 16, 1–32 (2013) CrossRef
31.
Potters, M., Bouchaud, J.-P.: More statistical properties of order books and price impact. Physica A 324, 133–140 (2003). Proceedings of the International Econophysics Conference MATHCrossRef
32.
Predoiu, S., Shaikhet, G., Shreve, S.: Optimal execution in a general one-sided limit-order book. SIAM J. Financ. Math. 2, 183–212 (2011) MATHMathSciNetCrossRef
33.
Robert, C.Y., Rosenbaum, M.: A new approach for the dynamics of ultra-high-frequency data: the model with uncertainty zones. J. Financ. Econom. 9, 344–366 (2011) CrossRef
34.
35.
Tóth, B., Palit, I., Lillo, F., Farmer, J.D.: Why is order flow so persistent? J. Econ. Dyn. Control 51, 218–239 (2015) CrossRef
36.
Zheng, B., Roueff, F., Abergel, F.: Modelling bid and ask prices using constrained Hawkes processes: ergodicity and scaling limit. SIAM J. Financ. Math. 5, 99–136 (2014) MATHMathSciNetCrossRef
Metadata
Title
Dynamic optimal execution in a mixed-market-impact Hawkes price model
Authors
Aurélien Alfonsi
Pierre Blanc
Publication date
01-01-2016
Publisher
Springer Berlin Heidelberg
Published in
Finance and Stochastics / Issue 1/2016
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI
https://doi.org/10.1007/s00780-015-0282-y

Other articles of this Issue 1/2016

Finance and Stochastics 1/2016 Go to the issue

OriginalPaper

Weakly time consistent concave valuations and their dual representations

OriginalPaper

Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

OriginalPaper

Universal arbitrage aggregator in discrete-time markets under uncertainty

OriginalPaper

Model-independent superhedging under portfolio constraints

OriginalPaper

Facelifting in utility maximization

OriginalPaper

Superreplication when trading at market indifference prices