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Optimal liquidation problem in illiquid markets

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  • Sadoghi, Amirhossein
  • Vecer, Jan

Abstract

In this research, we develop a trading strategy for the optimal liquidation problem of large-order trading, with different market microstructures, in an illiquid market. We formulate the liquidation problem as a discrete-time Markov decision process. In this market, the flow of liquidity events can be viewed as a point process with stochastic intensity. Based on this fact, we model the price impact as a linear function of a self-exciting dynamic process. Our trading algorithm is designed in such a way that when no favourite orders arrive in the Limit Order Book (LOB), the optimal solution takes offers from the lower levels of the LOB. This solution might contradict conventional optimal execution methods, which only trade with the best available limit orders; however, our findings show that the proposed strategy may reduce final inventory costs by preventing orders not being filled at earlier trading times. Furthermore, the results indicate that an optimal trading strategy is dependent on characteristics of the market microstructure.

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  • Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:3:p:1050-1066
    DOI: 10.1016/j.ejor.2021.05.020
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    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    3. Jean Tirole, 2011. "Illiquidity and All Its Friends," Journal of Economic Literature, American Economic Association, vol. 49(2), pages 287-325, June.
    4. Hasbrouck, Joel, 1991. "Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
    5. Olivier Guéant, 2015. "General Intensity Shapes in Optimal Liquidation," Post-Print hal-01393116, HAL.
    6. Kenneth A. Kavajecz, 1999. "A Specialist's Quoted Depth and the Limit Order Book," Journal of Finance, American Finance Association, vol. 54(2), pages 747-771, April.
    7. Michael J. Barclay & Terrence Hendershott & D. Timothy McCormick, 2003. "Competition among Trading Venues: Information and Trading on Electronic Communications Networks," Journal of Finance, American Finance Association, vol. 58(6), pages 2637-2666, December.
    8. Tarun Chordia & Richard Roll & Avanidhar Subrahmanyam, 2001. "Market Liquidity and Trading Activity," Journal of Finance, American Finance Association, vol. 56(2), pages 501-530, April.
    9. Emmanuel Bacry & Thibault Jaisson & Jean--François Muzy, 2016. "Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1179-1201, August.
    10. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    11. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    12. Alfonso Dufour & Robert F. Engle, 2000. "Time and the Price Impact of a Trade," Journal of Finance, American Finance Association, vol. 55(6), pages 2467-2498, December.
    13. Shleifer, Andrei & Summers, Lawrence H, 1990. "The Noise Trader Approach to Finance," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 19-33, Spring.
    14. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
    15. Kempf, Alexander & Korn, Olaf, 1999. "Market depth and order size1," Journal of Financial Markets, Elsevier, vol. 2(1), pages 29-48, February.
    16. Grossman, Sanford J & Miller, Merton H, 1988. " Liquidity and Market Structure," Journal of Finance, American Finance Association, vol. 43(3), pages 617-637, July.
    17. Cai, Fang & Han, Song & Li, Dan & Li, Yi, 2019. "Institutional herding and its price impact: Evidence from the corporate bond market," Journal of Financial Economics, Elsevier, vol. 131(1), pages 139-167.
    18. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    19. Jonathan Brogaard & Terrence Hendershott & Ryan Riordan, 2019. "Price Discovery without Trading: Evidence from Limit Orders," Journal of Finance, American Finance Association, vol. 74(4), pages 1621-1658, August.
    20. Angelos Dassios & Hongbiao Zhao, 2017. "Efficient Simulation of Clustering Jumps with CIR Intensity," Operations Research, INFORMS, vol. 65(6), pages 1494-1515, December.
    21. Ha, Youngmin & Zhang, Hai, 2020. "Algorithmic trading for online portfolio selection under limited market liquidity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1033-1051.
    22. Monika Mrázová & J. Peter Neary, 2017. "Not So Demanding: Demand Structure and Firm Behavior," American Economic Review, American Economic Association, vol. 107(12), pages 3835-3874, December.
    23. Leonid Kogan & Stephen A. Ross & Jiang Wang & Mark M. Westerfield, 2006. "The Price Impact and Survival of Irrational Traders," Journal of Finance, American Finance Association, vol. 61(1), pages 195-229, February.
    24. D. V. Lindley, 1961. "Dynamic Programming and Decision Theory," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 10(1), pages 39-51, March.
    25. Nicole Bäuerle & Ulrich Rieder, 2009. "MDP algorithms for portfolio optimization problems in pure jump markets," Finance and Stochastics, Springer, vol. 13(4), pages 591-611, September.
    26. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    27. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.
    28. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    29. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    30. 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.
    31. Garman, Mark B., 1976. "Market microstructure," Journal of Financial Economics, Elsevier, vol. 3(3), pages 257-275, June.
    32. Jingnan Chen & Liming Feng & Jiming Peng & Yinyu Ye, 2014. "Analytical Results and Efficient Algorithm for Optimal Portfolio Deleveraging with Market Impact," Operations Research, INFORMS, vol. 62(1), pages 195-206, February.
    33. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    34. Xavier Gabaix, 2016. "Power Laws in Economics: An Introduction," Journal of Economic Perspectives, American Economic Association, vol. 30(1), pages 185-206, Winter.
    35. 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, February.
    36. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    37. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    38. K. Giesecke & H. Kakavand & M. Mousavi, 2011. "Exact Simulation of Point Processes with Stochastic Intensities," Operations Research, INFORMS, vol. 59(5), pages 1233-1245, October.
    39. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    40. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 159-188.
    41. Andrei Kirilenko & Albert S. Kyle & Mehrdad Samadi & Tugkan Tuzun, 2017. "The Flash Crash: High-Frequency Trading in an Electronic Market," Journal of Finance, American Finance Association, vol. 72(3), pages 967-998, June.
    42. Vijay V. Desai & Vivek F. Farias & Ciamac C. Moallemi, 2012. "Pathwise Optimization for Optimal Stopping Problems," Management Science, INFORMS, vol. 58(12), pages 2292-2308, December.
    43. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    44. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    45. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
    46. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    47. Ting, Christopher & Warachka, Mitch & Zhao, Yonggan, 2007. "Optimal liquidation strategies and their implications," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1431-1450, April.
    48. Pierre Collin-Dufresne & Vyacheslav Fos, 2015. "Do Prices Reveal the Presence of Informed Trading?," Journal of Finance, American Finance Association, vol. 70(4), pages 1555-1582, August.
    49. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    50. Naveed Chehrazi & Peter W. Glynn & Thomas A. Weber, 2019. "Dynamic Credit-Collections Optimization," Management Science, INFORMS, vol. 67(6), pages 2737-2769, June.
    51. Chordia, Tarun & Subrahmanyam, Avanidhar & Tong, Qing, 2014. "Have capital market anomalies attenuated in the recent era of high liquidity and trading activity?," Journal of Accounting and Economics, Elsevier, vol. 58(1), pages 41-58.
    52. Easley, David & O'Hara, Maureen, 1987. "Price, trade size, and information in securities markets," Journal of Financial Economics, Elsevier, vol. 19(1), pages 69-90, September.
    53. 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, February.
    54. Gerry Tsoukalas & Jiang Wang & Kay Giesecke, 2019. "Dynamic Portfolio Execution," Management Science, INFORMS, vol. 67(5), pages 2015-2040, May.
    55. Philip, R., 2020. "Estimating permanent price impact via machine learning," Journal of Econometrics, Elsevier, vol. 215(2), pages 414-449.
    56. Goldstein, Michael A. & A. Kavajecz, Kenneth, 2000. "Eighths, sixteenths, and market depth: changes in tick size and liquidity provision on the NYSE," Journal of Financial Economics, Elsevier, vol. 56(1), pages 125-149, April.
    57. Comerton-Forde, Carole & Putniņš, Tālis J., 2015. "Dark trading and price discovery," Journal of Financial Economics, Elsevier, vol. 118(1), pages 70-92.
    58. Yonghui Huang & Xianping Guo, 2020. "Multiconstrained Finite-Horizon Piecewise Deterministic Markov Decision Processes with Unbounded Transition Rates," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 641-659, May.
    59. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
    60. Huang, Yonghui & Guo, Xianping, 2011. "Finite horizon semi-Markov decision processes with application to maintenance systems," European Journal of Operational Research, Elsevier, vol. 212(1), pages 131-140, July.
    61. Ragnar Norberg, 2004. "Vasiček Beyond The Normal," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 585-604, October.
    62. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    63. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    64. Michael J. Barclay & Terrence Hendershott & D. Timothy McCormick, 2003. "Competition among Trading Venues: Information and Trading on Electronic Communications Networks," Journal of Finance, American Finance Association, vol. 58(6), pages 2637-2665, December.
    65. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    66. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    67. Charles Cao & Oliver Hansch & Xiaoxin Wang, 2008. "Order Placement Strategies In A Pure Limit Order Book Market," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 31(2), pages 113-140, June.
    68. John W. Mamer, 1986. "Successive Approximations for Finite Horizon, Semi-Markov Decision Processes with Application to Asset Liquidation," Operations Research, INFORMS, vol. 34(4), pages 638-644, August.
    69. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    70. Chen, Jingnan & Feng, Liming & Peng, Jiming, 2015. "Optimal deleveraging with nonlinear temporary price impact," European Journal of Operational Research, Elsevier, vol. 244(1), pages 240-247.
    71. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    72. Pierre Collin-Dufresne & Vyacheslav Fos, 2013. "Do Prices Reveal the Presence of Informed Trading?," Swiss Finance Institute Research Paper Series 13-69, Swiss Finance Institute, revised Sep 2015.
    73. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    74. Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
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