Optimal Execution in Illiquid Market with the Absence of Price Manipulation

Seiya Kuno¹, Masamitsu Ohnishi²

¹Center for the Study of Finance and Insurance, Osaka University, Osaka, Japan.
²Graduate School of Economics, Osaka University, Osaka, Japan.

DOI: 10.4236/jmf.2015.51001                

Abstract

This article shows the execution performance of the risk-averse institutional trader with constant absolute risk aversion (CARA) type utility by using the condition of no price manipulation defined in the risk neutral sense. From two linear price impact models both satisfying that condition, we have derived the unique explicit optimal execution strategy calculated backwardly with dynamic programming equations. And our study shows that the optimal execution strategy exists in the static class. The derived solution can be decomposed into mainly two components, each giving an explanation of the property of optimal execution volume. Moreover we propose two conditions in order to compare the performance of these two price models, and illustrate that the performances of the two models are surprisingly different under certain conditions.

Keywords

Optimal Execution, Price Manipulation, Algorithmic Trading

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	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. http://dx.doi.org/10.1137/110822098
[2]	Almgren, R. and Chriss, N. (2000) Optimal Execution of Portfolio Transactions. Journal of Risk, 3, 5-39.
[3]	Huberman, G. and Stanzl, W. (2005) Optimal Liquidity Trading. Review of Finance, 9, 165-200. http://dx.doi.org/10.1007/s10679-005-7591-5
[4]	Gatheral, J. (2010) No-Dynamic-Arbitrage and Market Impact. Quantitative Finance, 10,749-759. http://dx.doi.org/10.1080/14697680903373692
[5]	Obizhaeva, A. and Wang, J. (2013) Optimal Trading Strategy and Supply/Demand Dynamics. Journal of Financial Markets, 16, 1-32. http://dx.doi.org/10.1016/j.finmar.2012.09.001
[6]	Bouchaud, J.-P., Farmer, J.D. and Lillo, F. (2009) How Markets Slowly Digest Changes in Supply and Demand. Handbook of Financial Markets: Dynamics and Evolution, Elsevier, Berlin.
[7]	Schied, A., Schöneborn, T. and Teharanci, M. (2010) Optimal Basket Liquidation for CARA Investors Is Deterministic. Applied Mathematical Finance, 17, 471-489. http://dx.doi.org/10.1080/13504860903565050
[8]	Bertsimas, D. and Lo, A. (1998) Optimal Control of Execution Costs. Journal of Financial Markets, 1, 1-50. http://dx.doi.org/10.1137/S0363012995291609
[9]	Huberman, G. and Stanzl, W. (2004) Price Manipulation and Quasi-Arbitrage. Econometrica, 74, 1247-1275. http://dx.doi.org/10.1111/j.1468-0262.2004.00531.x
[10]	Kunou, S. and Ohnishi, M. (2010) Optimal Execution Strategy with Price Impact. Research Institute for Mathematical Sciences (RIMS) Kokyuroku, 1645, 234-247.
[11]	Lorenz, C. and Schied, A. (2013) Drift Dependence of Optimal Trade Execution Strategies under Transient Price Impact. Finance and Stochastics, 17, 743-770. http://dx.doi.org/10.1007/s00780-013-0211-x
[12]	Almgren, R., Thum, C., Hauptmann, E. and Li, H. (2005) Equity Market Impact. Risk, 18, 57-62.
[13]	Bouchaud, J.-P., Mézard, M. and Potters, M. (2004) Statistical Properties of Stock Order Books: Empirical Results and Models. Quantitative Finance, 2, 251-256. http://dx.doi.org/10.1088/1469-7688/2/4/301