IDEAS home Printed from
   My bibliography  Save this article

Asymptotic analysis of hedging errors in models with jumps


  • Tankov, Peter
  • Voltchkova, Ekaterina


Most authors who studied the problem of option hedging in incomplete markets, and, in particular, in models with jumps, focused on finding the strategies that minimize the residual hedging error. However, the resulting strategies are usually unrealistic because they require a continuously rebalanced portfolio, which is impossible to achieve in practice due to transaction costs. In reality, the portfolios are rebalanced discretely, which leads to a 'hedging error of the second type', due to the difference between the optimal portfolio and its discretely rebalanced version. In this paper, we analyze this second hedging error and establish a limit theorem for the renormalized error, when the discretization step tends to zero, in the framework of general Itô processes with jumps. The results are applied to the problem of hedging an option with a discontinuous pay-off in a jump-diffusion model.

Suggested Citation

  • Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
  • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:2004-2027

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    2. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123.
    3. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112,
    4. Geiss, Christel & Geiss, Stefan, 2006. "On an approximation problem for stochastic integrals where random time nets do not help," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 407-422, March.
    5. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    6. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    7. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Thai Huu Nguyen & Serguei Pergamenschchikov, 2015. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Papers 1505.02627,
    2. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    3. Mats Brod'en & Magnus Wiktorsson, 2010. "Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy," Papers 1004.4526,
    4. Mats Brod'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709,
    5. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833,, revised Jul 2017.
    6. Masaaki Fukasawa, 2012. "Efficient Discretization of Stochastic Integrals," Papers 1204.0637,
    7. Takafumi Amaba, 2014. "A Discrete-Time Clark-Ocone Formula for Poisson Functionals," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(2), pages 97-120, May.
    8. Huu Thai Nguyen & Serguei Pergamenchtchikov, 2014. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Working Papers hal-00979199, HAL.
    9. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2015. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," School of Economics Working Papers 2015-17, University of Adelaide, School of Economics.


    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:eee:spapps:v:119:y:2009:i:6:p:2004-2027. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.