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

Finance and Stochastics

Volumn 20, Issue 1, 2016, Pages 183-218

  Alfonsi, Aurélien ^a   Blanc, Pierre ^a  

^a INRIA   (France)

Author keywords

Hawkes processes; High frequency trading; Market impact model; Market microstructure; Optimal execution; Price manipulations

Indexed keywords

EID: 84953839323     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-015-0282-y     Document Type: Article

References (36)

1. Abergel, F., Jedidi, A.: A mathematical approach to order book modeling. Int. J. Theor. Appl. Finance 16, 1350025 (2013)
2. Alfonsi, A., Fruth, A., Schied, A.: Optimal execution strategies in limit order books with general shape functions. Quant. Finance 10, 143–157 (2010)
3. Alfonsi, A., Schied, A.: Capacitary measures for completely monotone kernels via singular control. SIAM J. Control Optim. 51, 1758–1780 (2013)
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)
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)
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)
8. Bacry, E., Muzy, J.-F.: Hawkes model for price and trades high-frequency dynamics. Quant. Finance 14, 1147–1166 (2014)
9. Bayraktar, E., Ludkovski, M.: Optimal trade execution in illiquid markets. Math. Finance 21, 681–701 (2011)
10. Bertsimas, D., Lo, A.: Optimal control of execution costs. J. Financ. Mark. 1, 1–50 (1998)
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)
12. Cont, R., de Larrard, A.: Price dynamics in a Markovian limit order market. SIAM J. Financ. Math. 4, 1–25 (2013)
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)
15. Donier, J.: Market impact with autocorrelated order flow under perfect competition (2012). Unpublished. Available online: http://arxiv.org/abs/1212.4770
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)
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)
18. Farmer, J.D., Gerig, A., Lillo, F., Waelbroeck, H.: How efficiency shapes market impact. Quant. Finance 13, 1743–1758 (2013)
19. Filimonov, V., Sornette, D.: Quantifying reflexivity in financial markets: toward a prediction of flash crashes. Phys. Rev. E 85, 056108 (2012)
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)
21. Gatheral, J.: No-dynamic-arbitrage and market impact. Quant. Finance 10, 749–759 (2010)
22. Gatheral, J., Schied, A., Slynko, A.: Transient linear price impact and Fredholm integral equations. Math. Finance 22, 445–474 (2012)
23. Guéant, O.: Optimal execution and block trade pricing: a general framework. Appl. Math. Finance 22, 336–365 (2015)
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)
25. Hawkes, A.G.: Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 83–90 (1971)
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)
27. Huberman, G., Stanzl, W.: Price manipulation and quasi-arbitrage. Econometrica 72, 1247–1275 (2004)
28. Thibault, J., Rosenbaum, M.: Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab. 25, 600–631 (2015)
29. Mastromatteo, I., Tóth, B., Bouchaud, J.-P.: Agent-based models for latent liquidity and concave price impact. Phys. Rev. E 89, 042805 (2014)
30. Obizhaeva, A., Wang, J.: Optimal trading strategy and supply/demand dynamics. J. Financ. Mark. 16, 1–32 (2013)
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
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)
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)
34. Stoikov, S., Waeber, R.: Optimal asset liquidation using limit order book information (2012). Preprint. SSRN eLibrary. Available online: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2113827
35. Tóth, B., Palit, I., Lillo, F., Farmer, J.D.: Why is order flow so persistent? J. Econ. Dyn. Control 51, 218–239 (2015)
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)