A Fokker-Planck description for the queue dynamics of large tick stocks
AbstractMotivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the drift and diffusion depends on the volume present on both sides of the spread. "Jump" events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on best quotes. One of our central finding is the the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1304.6819.
Date of creation: Apr 2013
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-27 (All new papers)
- NEP-FMK-2013-04-27 (Financial Markets)
- NEP-MST-2013-04-27 (Market Microstructure)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Avellaneda, Marco & Reed, Josh & Stoikov, Sasha, 2011. "Forecasting prices from level-I quotes in the presence of hidden liquidity," Algorithmic Finance, IOS Press, vol. 1(1), pages 35-43.
- Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
- Aim\'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Papers 1305.6323, arXiv.org, revised Mar 2014.
- Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2013. "Simulating and analyzing order book data: The queue-reactive model," Papers 1312.0563, arXiv.org.
- Aurélien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Working Papers hal-00971369, HAL.
- Aur\'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.