Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-11T08:46:47.253Z Has data issue: false hasContentIssue false

22 - Dynamical Models of Market Impact and Algorithms for Order Execution

from PART VII - ALGORITHMIC TRADING

Published online by Cambridge University Press:  05 June 2013

By
Jim Gatheral  and
Alexander Schied
Edited by
Jean-Pierre Fouque  and
Joseph A. Langsam
Jim Gatheral
Affiliation:
Baruch College
Alexander Schied
Affiliation:
University of Mannheim
Jean-Pierre Fouque
Affiliation:
University of California, Santa Barbara
Joseph A. Langsam
Affiliation:
University of Maryland, College Park
Get access

Summary

Abstract In this chapter, we review recent work on the regularity of dynamical market impact models and their associated optimal order execution strategies. In particular, we address the question of the stability and existence of optimal strategies, showing that in a large class of models, there is price manipulation and no well-behaved optimal order execution strategy. We also address issues arising from the use of dark pools and predatory trading.

Introduction

Market impact refers to the fact that the execution of a large order influences the price of the underlying asset. Usually, this influence results in an adverse effect creating additional execution costs for the investor who is executing the trade. In some cases, however, generating market impact can also be the primary goal, e.g., when certain central banks buy government bonds in an attempt to lower the corresponding interest rates.

Understanding market impact and optimizing trading strategies to minimize market impact has long been an important goal for large investors. There is typically insufficient liquidity to permit immediate execution of large orders without eating into the limit order book. Thus, to minimize the cost of trading, large trades are split into a sequence of smaller trades, which are then spread out over a certain time interval.

Type
Chapter
Information
Handbook on Systemic Risk , pp. 579 - 602
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alfonsi, A., Fruth, A. and Schied, A. (2008). Constrained portfolio liquidation in a limit order book model. Banach Center Publications 83 9–25.Google Scholar
Alfonsi, A., Fruth, A. and Schied, A. (2010). Optimal execution strategies in limit order books with general shape functions. Quantitative Finance 10 143–157.CrossRefGoogle Scholar
Alfonsi, A. and Schied, A. (2010). Optimal trade execution and absence of price manipulations in limit order book models. SIAM Journal on Financial Mathematics 1 490–522.CrossRefGoogle Scholar
Alfonsi, A. and Schied, A. (2012). Capacitary measures for completely monotone kernels via singular control. Preprint. http://ssrn.com/abstract=1983943.Google Scholar
Alfonsi, A., Schied, A. and Slynko, A. (2012). Order book resilience, price manipulation, and the positive portfolio problem. SIAM Journal on Financial Mathematics 3, 511–533.CrossRefGoogle Scholar
Almgren, R. (2003). Optimal execution with nonlinear impact functions and trading-enhanced risk. Applied Mathematical Finance 10 1–18.CrossRefGoogle Scholar
Almgren, R. and Chriss, N. (1999). Value under liquidation. Risk 12 61–63.Google Scholar
Almgren, R. and Chriss, N. (2000). Optimal execution of portfolio transactions. Journal of Risk 3 5–39.Google Scholar
Almgren, R., Thum, C., Hauptmann, E. and Li, H. (2005). Direct estimation of equity market impact. Risk 18(7), 58–62.Google Scholar
Avellaneda, M. and Stoikov, S. (2008). High-frequency trading in a limit order book. Quantitative Finance 8(3), 217–224.CrossRefGoogle Scholar
Bank, P. and Baum, D. (2004). Hedging and portfolio optimization in financial markets with a large trader. Mathematical Finance 14(1), 1–18.CrossRefGoogle Scholar
Baum, D. (2001). Realisierbarer Portfoliowert in Finanzmärtken. Ph.D. thesis, Humboldt University of Berlin.Google Scholar
Bayraktar, E. and Ludkovski, M. (2011). Liquidation in limit order books with controlled intensity. To appear in Mathematical Finance.Google Scholar
Bertsimas, D. and Lo, A. (1998). Optimal control of execution costs. Journal of Financial Markets 1 1–50.CrossRefGoogle Scholar
Bochner, S. (1932). Vorlesungen über Fouriersche Integrale, Akademische Verlagsgesellschaft, Leipzig.Google Scholar
Bouchard, B., Dang, N.-M. and Lehalle, C.-A. (2011). Optimal control of trading algorithms: a general impulse control approach. SIAM Journal on Financial Mathematics 2(1), 404–438.CrossRefGoogle Scholar
Bouchaud, J.-P. (2010). Price impact. In Encyclopedia of Quantitative Finance, R., Cont (ed). John Wiley & Sons, Ltd.Google Scholar
Bouchaud, J.-P., Gefen, Y., Potters, M. and Wyart, M. (2004). Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes. Quantitative Finance 4 176–190.CrossRefGoogle Scholar
Brunnermeier, M. K. and Pedersen, L. H. (2005). Predatory trading. Journal of Finance 60(4), 1825–1863.CrossRefGoogle Scholar
Carathéodory, C. (1907). Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen. Mathematische Annalen 64 95–115.CrossRefGoogle Scholar
Carlin, B. I., Lobo, M. S. and Viswanathan, S. (2007). Episodic liquidity crises: cooperative and predatory trading. Journal of Finance 65 2235–2274.Google Scholar
Çetin, U., Jarrow, R. A. and Protter, P. (2004). Liquidity risk and arbitrage pricing theory. Finance and Stochastics 8(3), 311–341.CrossRefGoogle Scholar
CFTC-SEC (2010). Findings regarding the market events of May 6, 2010. Report.
Cont, R. and de Larrard, A. (2010). Linking volatility with order flow: heavy traffic approximations and diffusion limits of order book dynamics. Preprint.Google Scholar
Cont, R. and de Larrard, A. (2011). Price dynamics in a Markovian limit order market. Preprint.Google Scholar
Cont, R., Kukanov, A. and Stoikov, S. (2010). The price impact of order book events. Preprint. http://ssrn.com/abstract=1712822.Google Scholar
Cont, R., Stoikov, S. and Talreja, R. (2010). A stochastic model for order book dynamics. Operations Research 58(3) 549–563.CrossRefGoogle Scholar
Forsyth, P., Kennedy, J., Tse, T. S. and Windclif, H. (2009). Optimal trade execution: a mean-quadratic-variation approach. Journal of Economic Dynamics and Control 36, 1971–1991.Google Scholar
Frey, R. and Stremme, A. (1997). Market volatility and feedback effects from dynamic hedging. Mathematical Finance 7(4), 351–374.CrossRefGoogle Scholar
Fruth, A., Schöneborn, T. and Urusov, M. (2011). Optimal trade execution and price manipulation in order books with time-varying liquidity. Preprint. http://ssrn.com/paper=1925808.Google Scholar
Gatheral, J. (2010). No-dynamic-arbitrage and market impact. Quantitative Finance 10 749–759.CrossRefGoogle Scholar
Gatheral, J. and Schied, A. (2011). Optimal trade execution under geometric Brownian motion in the Almgren and Chriss framework. International Journal of Theoretical and Applied Finance 14 353–368.CrossRefGoogle Scholar
Gatheral, J., Schied, A. and Slynko, A. (2011). Exponential resilience and decay of market impact. In Econophysics of Order-Driven Markets, F., Abergel, B., Chakrabarti, A., Chakraborti and M., Mitra, (eds). Springer-Verlag, 225–236.Google Scholar
Gatheral, J., Schied, A. and Slynko, A. (2012). Transient linear price impact and Fredholm integral equations. Mathematical Finance 22, 445–474.CrossRefGoogle Scholar
Gökay, S., Roch, A. and Soner, H. M. (2011). Liquidity models in continuous and discrete time. In Advanced Mathematical Methods for Finance, G., di Nunno and B., Øksendal (eds). Springer-Verlag, 333–366.Google Scholar
Guéant, O., Lehalle, C.-A. and Tapia, J. F. (2012). Optimal portfolio liquidation with limit orders. SIAM Journal on Financial Mathematics 3, 740–764.CrossRefGoogle Scholar
Huberman, G. and Stanzl, W. (2004). Price manipulation and quasi-arbitrage. Econometrica 72 (4) 1247–1275.CrossRefGoogle Scholar
Kato, T. (2011). An optimal execution problem with market impact. Preprint.Google Scholar
Kharroubi, I. and Pham, H. (2010). Optimal portfolio liquidation with execution cost and risk. SIAM Journal on Financial Mathematics 1 897–931.CrossRefGoogle Scholar
Klöck, F., Schied, A. and Sun, Y. (2011). Existence and absence of price manipulation in a market impact model with dark pool. Preprint. http://ssrn.com/paper=1785409Google Scholar
Konishi, H. and Makimoto, N. (2001). Optimal slice of a block trade. Journal of Risk 3 (4) 33–51.CrossRefGoogle Scholar
Kratz, P. and Schöneborn, T. (2010). Optimal liquidation in dark pools. Preprint. http://ssrn.com/abstract=1344583.Google Scholar
Laruelle, S., Lehalle, C.-A. and Pagès, G. (2010). Optimal split of orders across liquidity pools: a stochastic algorithm approach. Preprint. http://arxiv.org/abs/0910.1166.Google Scholar
Lehalle, C.-A. (2012). Market micro-structure knowledge needed for controlling an intraday trading process. Handbook on Systemic Risk, J.-P., Fouque and J., Langsam (eds). Cambridge University Press.Google Scholar
Lehalle, C.-A. and Dang, N. (2010). Rigorous post-trade market impact measurement and the price formation process. Trading 1 108–114.Google Scholar
Lehalle, C.-A., Guéant, O. and Razafinimanana, J. (2011). High frequency simulations of an order book: a two-scales approach. In Econophysics of Order-driven Markets, F., Abergel, B., Chakrabarti, A., Chakraborti and M., Mitra (eds). Springer-Verlag.Google Scholar
Lorenz, C. and Schied, A. (2012). Drift dependence of optimal order execution strategies under transient price impact. Preprint. http://ssrn.com/abstract=1993103.Google Scholar
Lorenz, J. and Almgren, R. (2011). Mean-variance optimal adaptive execution. Applied Mathematical Finance 18(5), 395–422.CrossRefGoogle Scholar
Madhavan, A. (2000). Market microstructure: a survey. Journal of Financial Markets 3(3) 205–258.CrossRefGoogle Scholar
Moro, E., Vicente, J., Moyano, L. G., Gerig, A., Farmer, J. D., Vaglica, G., Lillo, F. and Mantegna, R. N. (2009). Market impact and trading profile of hidden orders in stock markets. Physical ReviewE 80(6) 066–102.Google ScholarPubMed
Obizhaeva, A. and Wang, J. (2013). Optimal trading strategy and supply/demand dynamics. Journal of Financial Markets 16, 1–32.CrossRefGoogle Scholar
Pham, H., Ly Vath, V. and Zhou, X. Y. (2009). Optimal switching over multiple regimes. SIAM Journal on Control and Optimization 48(4), 2217–2253.CrossRefGoogle Scholar
Pólya, G. (1949). Remarks on characteristic functions. In Proceedings of the Berkeley Symposium of Mathematical Statistics and Probability, J., Neyman (ed). University of California Press, 115–123.Google Scholar
Predoiu, S., Shaikhet, G. and Shreve, S. (2011). Optimal execution in a general one-sided limit-order book. SIAM Journal on Financial Mathematics 2 183–212.CrossRefGoogle Scholar
Roch, A. (2011). Liquidity risk, price impacts and the replication problem. Finance and Stochastics 15 399–419.CrossRefGoogle Scholar
Roch, A. and Soner, H. (2011). Resilient price impact of trading and the cost of illiquidity. Preprint. http://ssrn.com/paper=1923840.Google Scholar
Schied, A. (2011). Robust strategies for optimal order execution in the Almgren–Chriss framework. Preprint. http://ssrn.com/paper=1991097.Google Scholar
Schied, A. and Schöneborn, T. (2009). Risk aversion and the dynamics of optimal trading strategies in illiquid markets. Finance and Stochastics 13 181–204.CrossRefGoogle Scholar
Schied, A., Schöneborn, T. and Tehranchi, M. (2010). Optimal basket liquidation for CARA investors is deterministic. Applied Mathematical Finance 17 471–489.CrossRefGoogle Scholar
Schöneborn, T. (2008). Trade Execution in Illiquid Markets. Optimal Stochastic Control and Multi-Agent Equilibria. Ph.D. thesis, TU Berlin.Google Scholar
Schöneborn, T. (2011). Adaptive Basket Liquidation. Preprint. http://ssrn.com/paper=1343985.Google Scholar
Schöneborn, T. and Schied, A. (2009). Liquidation in the face of adversity: stealth vs. sunshine trading. Preprint.Google Scholar
Toeplitz, O. (1911). Zur Theorie der quadratischen und bilinearen Formen von unendlich vielen Veränderlichen. Mathematische Annalen 70 351–376.CrossRefGoogle Scholar
Tóth, B., Lempérière, Y., Deremble, C., de Lataillade, J., Kockelkoren, J. and Bouchaud, J.-P. (2011). Anomalous price impact and the critical nature of liquidity in financial markets. Physical Review X 1 021006.CrossRefGoogle Scholar
Weber, P. and Rosenow, B. (2005). Order book approach to price impact. Quantitative Finance 5 357–364.CrossRefGoogle Scholar
Weiss, A. (2009). Executing large orders in a microscopic market model. Preprint. http://arxiv.org/abs/0904.4131v2.Google Scholar
Young, W. H. (1913). On the Fourier series of bounded functions. Proceedings of the London Mathematical Society (2) 12 41–70.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×