IDEAS home Printed from https://ideas.repec.org/a/wsi/ijfexx/v04y2017i02n03ns242478631750030x.html
   My bibliography  Save this article

Hedging and pricing illiquid options with market impacts

Author

Listed:
  • Taiga Saito

    (Graduate School of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan)

Abstract

In this paper, we consider hedging and pricing of illiquid options on an untradable underlying asset, where an alternative asset is used as a hedging instrument. Particularly, we consider the situation where the trade price of the hedging instrument is subject to market impacts caused by the hedger and the liquidity costs paid as a spread from the mid price. Pricing illiquid options, which often appears in trading of structured products, is a critical issue in practice because of its difficulties in hedging mainly due to untradability of the underlying asset as well as the liquidity costs and market impacts of the hedging instrument. First, by setting the problem under a discrete time model, where the optimal hedging strategy is defined by the local risk-minimization, we present algorithms to obtain the option price along with the hedging strategy by an asymptotic expansion. Moreover, we provide numerical examples. This model enables the estimation of the effect of both the market impacts and the liquidity costs on option prices, which is important in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:02n03:n:s242478631750030x
    DOI: 10.1142/S242478631750030X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S242478631750030X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S242478631750030X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    2. Damien Lamberton & Huyên Pham & Martin Schweizer, 1998. "Local Risk-Minimization Under Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 585-612, August.
    3. Taiga Saito, 2015. "Self-financing strategy expression in general shape limit order book with market impacts in continuous time," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 1-19.
    4. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    5. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    6. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18, January.
    7. 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.
    8. 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.
    9. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    10. Frédéric Abergel & Grégoire Loeper, 2013. "Pricing and hedging contingent claims with liquidity costs and market impact," Working Papers hal-00802402, HAL.
    11. Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
    13. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Aur'elien Alfonsi & Alexander Schied & Florian Klock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Sep 2015.
    3. Hyoeun Lee & Kiseop Lee, 2020. "Optimal execution with liquidity risk in a diffusive order book market," Papers 2004.10951, arXiv.org.
    4. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    5. Jan Kallsen & Johannes Muhle-Karbe, 2014. "High-Resilience Limits of Block-Shaped Order Books," Papers 1409.7269, arXiv.org.
    6. Alexander Schied & Tao Zhang, 2013. "A market impact game under transient price impact," Papers 1305.4013, arXiv.org, revised May 2017.
    7. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2015. "Optimal Asset Liquidation with Multiplicative Transient Price Impact," Papers 1501.01892, arXiv.org, revised Apr 2017.
    8. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CARF F-Series CARF-F-360, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2015.
    9. 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.
    10. Arne Lokka & Junwei Xu, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes," Papers 2002.03376, arXiv.org, revised Sep 2020.
    11. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320, arXiv.org, revised Jan 2015.
    12. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CIRJE F-Series CIRJE-F-963, CIRJE, Faculty of Economics, University of Tokyo.
    13. Lokka, A. & Xu, Junwei, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model," LSE Research Online Documents on Economics 106977, London School of Economics and Political Science, LSE Library.
    14. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," Papers 1503.07007, arXiv.org, revised Sep 2015.
    15. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    16. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    17. Damiano Brigo & Federico Graceffa & Eyal Neuman, 2022. "Price impact on term structure," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 171-195, January.
    18. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org, revised Jun 2015.
    19. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Working Papers hal-03668669, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijfexx:v:04:y:2017:i:02n03:n:s242478631750030x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/worldscinet/ijfe .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.