IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1106.2095.html
   My bibliography  Save this paper

Duality and Convergence for Binomial Markets with Friction

Author

Listed:
  • Yan Dolinsky
  • Halil Mete Soner

Abstract

We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the super-replication cost in these models are obtained and used to prove the limit theorems. In particular, the existence of the liquidity premium for the continuous time limit of the model proposed in [6] is proved. Hence, this paper extends the previous convergence result of [13] to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the $G$-expectation of Peng as earlier proved by Kusuoka in [14].

Suggested Citation

  • Yan Dolinsky & Halil Mete Soner, 2011. "Duality and Convergence for Binomial Markets with Friction," Papers 1106.2095, arXiv.org.
    • Handle: RePEc:arx:papers:1106.2095
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1106.2095
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Prasad Chalasani & Somesh Jha, 2001. "Randomized Stopping Times and American Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 33-77, January.
    2. 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.
    3. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29, January.
    4. Yan DOLINSKY & Marcel NUTZ & Halil Mete SONER, 2011. "Weak Approximation of G-Expectations," Swiss Finance Institute Research Paper Series 11-09, Swiss Finance Institute.
    5. 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..
    6. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    7. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    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. Christian Bayer & Bezirgen Veliyev, 2014. "Utility Maximization In A Binomial Model With Transaction Costs: A Duality Approach Based On The Shadow Price Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-27.

    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. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
    2. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    3. 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.
    4. Robert Jarrow, 2018. "Asset market equilibrium with liquidity risk," Annals of Finance, Springer, vol. 14(2), pages 253-288, May.
    5. Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895, arXiv.org.
    6. Sergey Lototsky & Henry Schellhorn & Ran Zhao, 2016. "A String Model of Liquidity in Financial Markets," Papers 1608.05900, arXiv.org, revised Apr 2018.
    7. Olivier Guéant & Jiang Pu, 2017. "Option Pricing And Hedging With Execution Costs And Market Impact," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 803-831, July.
    8. Kraft, Holger & Kühn, Christoph, 2011. "Large traders and illiquid options: Hedging vs. manipulation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1898-1915.
    9. Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
    10. Alexandre F. Roch, 2008. "Liquidity Risk, Price Impacts and the Replication Problem," Papers 0812.2440, arXiv.org, revised Dec 2009.
    11. Lepinette, Emmanuel & Tran, Tuan, 2017. "Arbitrage theory for non convex financial market models," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3331-3353.
    12. Peter Bank & Yan Dolinsky & Selim Gokay, 2014. "Super-replication with nonlinear transaction costs and volatility uncertainty," Papers 1411.1229, arXiv.org, revised Jun 2015.
    13. Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 692-708, August.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    19. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2018. "Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-44, June.
    20. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.

    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:1106.2095. 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.