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Resilient Price Impact Of Trading And The Cost Of Illiquidity

Author

Listed:
  • ALEXANDRE ROCH

    (ESG UQAM, Department of Finance, 315, East Sainte-Catherine Street, Montréal H2X 3X2, Canada)

  • H. METE SONER

    (ETH Zürich, Department of Mathematics, HG G 54.3, Rämistrasse 101, 8092 Zürich, Switzerland;
    The Swiss Finance Institute, Switzerland)

Abstract

We construct a model for liquidity risk and price impacts in a limit order book setting with depth, resilience and tightness. We derive a wealth equation and a characterization of illiquidity costs. We show that we can separate liquidity costs due to depth and resilience from those related to tightness, and obtain a reduced model in which proportional costs due to the bid-ask spread is removed. From this, we obtain conditions under which the model is arbitrage free. By considering the standard utility maximization problem, this also allows us to obtain a stochastic discount factor and an asset pricing formula which is consistent with empirical findings (e.g., Brennan and Subrahmanyam (1996); Amihud and Mendelson (1986)). Furthermore, we show that in limiting cases for some parameters of the model, we derive many existing liquidity models present in the arbitrage pricing literature, including Çetin et al. (2004) and Rogers and Singh (2010). This offers a classification of different types of liquidity costs in terms of the depth and resilience of prices.

Suggested Citation

  • Alexandre Roch & H. Mete Soner, 2013. "Resilient Price Impact Of Trading And The Cost Of Illiquidity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-27.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:06:n:s0219024913500374
    DOI: 10.1142/S0219024913500374
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    Citations

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    Cited by:

    1. Ariel Neufeld & Mario Sikic, 2017. "Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty," Papers 1711.03875, arXiv.org, revised Apr 2019.
    2. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    3. Etienne Chevalier & Vathana Ly Vath & Simone Scotti & Alexandre Roch, 2016. "Optimal Execution Cost For Liquidation Through A Limit Order Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-26, February.
    4. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    5. Jan Kallsen & Johannes Muhle-Karbe, 2014. "High-Resilience Limits of Block-Shaped Order Books," Papers 1409.7269, arXiv.org.
    6. Ariel Neufeld & Mario Šikić, 2019. "Nonconcave robust optimization with discrete strategies under Knightian uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 229-253, October.
    7. Erhan Bayraktar & Thomas Cayé & Ibrahim Ekren, 2021. "Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 36-108, January.
    8. Ahmet Umur Ozsoy & Omur Uu{g}ur, 2023. "The QLBS Model within the presence of feedback loops through the impacts of a large trader," Papers 2311.06790, arXiv.org.
    9. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    10. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    11. Peter Bank & Moritz Vo{ss}, 2018. "Optimal investment with transient price impact," Papers 1804.07392, arXiv.org.
    12. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org, revised Mar 2015.
    13. Mazin A.M. Al Janabi, 2021. "Is optimum always optimal? A revisit of the mean‐variance method under nonlinear measures of dependence and non‐normal liquidity constraints," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 387-415, April.
    14. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    15. Taiga Saito, 2017. "Hedging and pricing illiquid options with market impacts," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
    16. H. Mete Soner & Mirjana Vukelja, 2016. "Utility maximization in an illiquid market in continuous time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 285-321, October.

    More about this item

    Keywords

    Liquidity risk; limit order books; asset pricing; utility maximization; resilience; price impacts; D40; G11; G12;
    All these keywords.

    JEL classification:

    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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