Optimal Portfolio Liquidation with Limit Orders
AbstractThis paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang, we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these two issues separately: they compute an optimal trading curve and they then send orders to the markets to try to follow it. The results obtained here solve simultaneously the two problems. As in a previous paper that solved the "intra-day market making problem", the interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive "fair price" and a Hamilton-Jacobi-Bellman equation is used to solve the problem involving both non-execution risk and price risk. Backtests are carried out to exemplify the use of our results, both on long periods of time (for the entire liquidation process) and on slices of 5 minutes (to follow a given trading curve).
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 1106.3279.
Date of creation: Jun 2011
Date of revision: Jul 2012
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
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.:
- E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2011.
"Modeling microstructure noise with mutually exciting point processes,"
- E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
- Gur Huberman & Werner Stanzl, 2005.
"Optimal Liquidity Trading,"
Review of Finance,
Springer, vol. 9(2), pages 165-200, 06.
- Foucault, Thierry & Menkveld, Albert, 2006.
"Competition for order flow and smart order routing systems,"
Les Cahiers de Recherche
831, HEC Paris.
- Thierry Foucault & Albert J. Menkveld, 2008. "Competition for Order Flow and Smart Order Routing Systems," Journal of Finance, American Finance Association, vol. 63(1), pages 119-158, 02.
- Foucault, Thierry & Menkveld, Albert J., 2006. "Competition for Order Flow and Smart Order Routing Systems," CEPR Discussion Papers 5523, C.E.P.R. Discussion Papers.
- 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.
- Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
- Schied, Alexander & Schoeneborn, Torsten, 2008.
"Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets,"
7105, University Library of Munich, Germany.
- Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
- Thomas Ho & Hans Stoll, .
"Optimal Dealer Pricing Under Transactions and Return Uncertainty,"
Rodney L. White Center for Financial Research Working Papers
27-79, Wharton School Rodney L. White Center for Financial Research.
- Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
- Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
- Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2009.
"Optimal split of orders across liquidity pools: a stochastic algorithm approach,"
- Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag\`es, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Papers 0910.1166, arXiv.org, revised May 2010.
- Olivier Gu\'eant, 2012. "Execution and block trade pricing with optimal constant rate of participation," Papers 1210.7608, arXiv.org, revised Dec 2013.
- Olivier Gu\'eant, 2012. "Optimal execution and block trade pricing: a general framework," Papers 1210.6372, arXiv.org, revised Jul 2013.
- Kovaleva, P. & Iori, G., 2012. "Optimal Trading Strategies in a Limit Order Market with Imperfect Liquidity," Working Papers 12/05, Department of Economics, City University London.
- Aur\'elien Alfonsi & Alexander Schied & Florian Kl\"ock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Oct 2013.
- Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
- Christopher Lorenz & Alexander Schied, 2012. "Drift dependence of optimal trade execution strategies under transient price impact," Papers 1204.2716, arXiv.org, revised Mar 2013.
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.