IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v14y2004i1p1-18.html
   My bibliography  Save this article

Hedging and Portfolio Optimization in Financial Markets with a Large Trader

Author

Listed:
  • Peter Bank
  • Dietmar Baum

Abstract

We introduce a general continuous‐time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter‐dependent semimartingales, and its mathematical analysis relies on the nonlinear integration theory of such semimartingale families. The Itô–Wentzell formula is used to prove absence of arbitrage for the large investor, and, using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:1:p:1-18
    DOI: 10.1111/j.0960-1627.2004.00179.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.0960-1627.2004.00179.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.0960-1627.2004.00179.x?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
    ---><---

    References listed on IDEAS

    as
    1. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    2. Robert A. Jarrow, 2008. "Market Manipulation, Bubbles, Corners, and Short Squeezes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 6, pages 105-130, World Scientific Publishing Co. Pte. Ltd..
    3. Robert A. Jarrow, 2008. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 7, pages 131-151, World Scientific Publishing Co. Pte. Ltd..
    4. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374, October.
    5. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    6. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    7. K. Ronnie Sircar & George Papanicolaou, 1998. "General Black-Scholes models accounting for increased market volatility from hedging strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 45-82.
    8. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    Full references (including those not matched with items on IDEAS)

    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. Sergey Lototsky & Henry Schellhorn & Ran Zhao, 2016. "A String Model of Liquidity in Financial Markets," Papers 1608.05900, arXiv.org, revised Apr 2018.
    2. Bank, Peter & Baum, Dietmar, 2002. "Hedging and portfolio optimization in illiquid financial markets," SFB 373 Discussion Papers 2002,53, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. David German & Henry Schellhorn, 2012. "A No-Arbitrage Model of Liquidity in Financial Markets involving Brownian Sheets," Papers 1206.4804, arXiv.org.
    4. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    5. Jinqiang Yang & Zhaojun Yang, 2012. "Arbitrage-free interval and dynamic hedging in an illiquid market," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1029-1039, May.
    6. Jarrow, Robert & Protter, Philip, 2005. "Large traders, hidden arbitrage, and complete markets," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2803-2820, November.
    7. Bertram Düring & Michel Fournié & Ansgar Jüngel, 2003. "High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 767-789.
    8. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    9. Ku, Hyejin & Lee, Kiseop & Zhu, Huaiping, 2012. "Discrete time hedging with liquidity risk," Finance Research Letters, Elsevier, vol. 9(3), pages 135-143.
    10. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    11. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29, January.
    12. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    13. Gill, Ryan & Lee, Kiseop & Song, Seongjoo, 2007. "Computation of estimates in segmented regression and a liquidity effect model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6459-6475, August.
    14. Sang-Hyeon Park & Kiseop Lee, 2020. "Hedging with Liquidity Risk under CEV Diffusion," Risks, MDPI, vol. 8(2), pages 1-12, June.
    15. Michael Gallmeyer & Duane Seppi, "undated". "Derivative Security Induced Price Manipulation," GSIA Working Papers 2000-E41, Carnegie Mellon University, Tepper School of Business.
    16. Chung, San-Lin & Liu, Wen-Rang & Tsai, Wei-Che, 2014. "The impact of derivatives hedging on the stock market: Evidence from Taiwan’s covered warrants market," Journal of Banking & Finance, Elsevier, vol. 42(C), pages 123-133.
    17. Salvatore Federico & Paul Gassiat, 2014. "Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 966-991, March.
    18. Elettra Agliardi & Rainer Andergassen, 2011. "(S,s)-adjustment Strategies and Hedging under Markovian Dynamics," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 36(2), pages 112-131, December.
    19. Elettra Agliardi & Rainer Andergassen, 2007. "(S,S)-Adjustment Strategies And Dynamic Hedging," Working Paper series 09_07, Rimini Centre for Economic Analysis.
    20. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.

    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:bla:mathfi:v:14:y:2004:i:1:p:1-18. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.