Optimal High Frequency Trading with limit and market orders
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders
References listed on IDEAS
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.:
- Erhan Bayraktar & Michael Ludkovski, 2014.
"Liquidation In Limit Order Books With Controlled Intensity,"
Wiley Blackwell, vol. 24(4), pages 627-650, October.
- Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
- Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
- Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
- Olivier Guéant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2013. "Dealing with the Inventory Risk. A solution to the market making problem," Post-Print hal-01393110, HAL.
- Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
- repec:dau:papers:123456789/7390 is not listed on IDEAS
- Sasha Stoikov & Mehmet Sağlam, 2009. "Option market making under inventory risk," Review of Derivatives Research, Springer, vol. 12(1), pages 55-79, April.
- Terrence Hendershott & Charles M. Jones & Albert J. Menkveld, 2011. "Does Algorithmic Trading Improve Liquidity?," Journal of Finance, American Finance Association, vol. 66(1), pages 1-33, 02.
- Hendershott, Terrence & Jones, Charles M. & Menkveld, Albert J., 2008. "Does algorithmic trading improve liquidity?," CFS Working Paper Series 2008/41, Center for Financial Studies (CFS).
- Luc Bauwens & David Veredas & Winfried Pohlmeier, 2005. "High frequency finance," ULB Institutional Repository 2013/136220, ULB -- Universite Libre de Bruxelles. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1106.5040. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.