Optimal execution strategies in limit order books with general shape functions
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.
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.:
- Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
- Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
- Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2004.
NBER Working Papers
10755, National Bureau of Economic Research, Inc.
- Brunnermeier, Markus K & Pedersen, Lasse Heje, 2004. "Predatory Trading," CEPR Discussion Papers 4639, C.E.P.R. Discussion Papers.
- Markus K. Brunnermeier & Lasse Heje Pederson, 2003. "Predatory trading," LSE Research Online Documents on Economics 24829, London School of Economics and Political Science, LSE Library.
- Markus K Brunnermeier & Lasse Heje Pederson, 2003. "Predatory Trading," FMG Discussion Papers dp441, Financial Markets Group.
- Lasse H. Pedersen & Markus Brunnermeier, 2004. "Predatory Trading," Econometric Society 2004 North American Winter Meetings 425, Econometric Society.
- Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
- Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003.
"Fluctuations and response in financial markets: the subtle nature of `random' price changes,"
cond-mat/0307332, arXiv.org, revised Aug 2003.
- Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Science & Finance (CFM) working paper archive 0307332, Science & Finance, Capital Fund Management.
- Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:0708.1756. 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 references are entirely missing, you can add them using this form.