IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0809.3824.html
   My bibliography  Save this paper

Time Consistent Dynamic Limit Order Books Calibrated on Options

Author

Listed:
  • Jocelyne Bion-Nadal

Abstract

In an incomplete financial market, the axiomatic of Time Consistent Pricing Procedure (TCPP), recently introduced, is used to assign to any financial asset a dynamic limit order book, taking into account both the dynamics of basic assets and the limit order books for options. Kreps-Yan fundamental theorem is extended to that context. A characterization of TCPP calibrated on options is given in terms of their dual representation. In case of perfectly liquid options, these options can be used as the basic assets to hedge dynamically. A generic family of TCPP calibrated on option prices is constructed, from cadlag BMO martingales.

Suggested Citation

  • Jocelyne Bion-Nadal, 2008. "Time Consistent Dynamic Limit Order Books Calibrated on Options," Papers 0809.3824, arXiv.org.
  • Handle: RePEc:arx:papers:0809.3824
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0809.3824
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    2. Jocelyne Bion-Nadal, 2007. "Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk," Papers math/0703074, arXiv.org.
    3. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    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. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.

    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. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    2. Cohen, Samuel N., 2012. "Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1601-1626.
    3. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    4. Schoeneborn, Torsten & Schied, Alexander, 2007. "Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision," MPRA Paper 5548, University Library of Munich, Germany.
    5. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    6. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    7. Yanhong Chen & Zachary Feinstein, 2022. "Set-valued dynamic risk measures for processes and for vectors," Finance and Stochastics, Springer, vol. 26(3), pages 505-533, July.
    8. Ernst, Cornelia & Stange, Sebastian & Kaserer, Christoph, 2012. "Measuring market liquidity risk - which model works best?," Journal of Financial Transformation, Capco Institute, vol. 35, pages 133-146.
    9. Csóka, Péter, 2017. "Fair risk allocation in illiquid markets," Finance Research Letters, Elsevier, vol. 21(C), pages 228-234.
    10. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    11. Villena, Marcelo J. & Reus, Lorenzo, 2016. "On the strategic behavior of large investors: A mean-variance portfolio approach," European Journal of Operational Research, Elsevier, vol. 254(2), pages 679-688.
    12. Tomasz R. Bielecki & Igor Cialenco & Hao Liu, 2023. "Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functions," Papers 2309.02570, arXiv.org, revised Sep 2023.
    13. 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.
    14. Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    15. Carlo Acerbi & Giacomo Scandolo, 2008. "Liquidity risk theory and coherent measures of risk," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 681-692.
    16. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    17. Erindi Allaj, 2014. "Risk measuring under liquidity risk," Papers 1412.6745, arXiv.org.
    18. Thomas Krabichler & Josef Teichmann, 2020. "A constraint-based notion of illiquidity," Papers 2004.12394, arXiv.org.
    19. Robert Jarrow, 2018. "Asset market equilibrium with liquidity risk," Annals of Finance, Springer, vol. 14(2), pages 253-288, May.
    20. Dolinsky, Yan & Zouari, Jonathan, 2021. "The value of insider information for super-replication with quadratic transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 394-416.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:0809.3824. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.