IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1004.4526.html
   My bibliography  Save this paper

Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy

Author

Listed:
  • Mats Brod'en
  • Magnus Wiktorsson

Abstract

Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches zero is analyzed. The results hinge to a great extent on a theorem stating that the difference between the hedge ratios normalized by the threshold level tends to a triangular distribution as the threshold level tends to zero.

Suggested Citation

  • Mats Brod'en & Magnus Wiktorsson, 2010. "Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy," Papers 1004.4526, arXiv.org.
    • Handle: RePEc:arx:papers:1004.4526
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1004.4526
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Takaki Hayashi & Per A. Mykland, 2005. "Evaluating Hedging Errors: An Asymptotic Approach," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 309-343, April.
    4. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    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. 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, arXiv.org, revised Jul 2017.
    2. Wang, Wensheng, 2019. "Asymptotics for discrete time hedging errors under fractional Black–Scholes models," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 160-170.
    3. Mats Brod'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709, arXiv.org.
    4. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    5. Masaaki Fukasawa, 2012. "Efficient Discretization of Stochastic Integrals," Papers 1204.0637, arXiv.org.
    6. Stefan Geiss & Emmanuel Gobet, 2010. "Fractional smoothness and applications in finance," Papers 1004.3577, arXiv.org.
    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. Stefan Geiss & Emmanuel Gobet, 2011. "Fractional smoothness and applications in Finance," Post-Print hal-00474803, HAL.
    9. 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.
    10. Asaf Cohen & Yan Dolinsky, 2022. "A scaling limit for utility indifference prices in the discretised Bachelier model," Finance and Stochastics, Springer, vol. 26(2), pages 335-358, April.
    11. Simon F'ecamp & Joseph Mikael & Xavier Warin, 2019. "Risk management with machine-learning-based algorithms," Papers 1902.05287, arXiv.org, revised Aug 2020.
    12. Asaf Cohen & Yan Dolinsky, 2021. "A Scaling Limit for Utility Indifference Prices in the Discretized Bachelier Model," Papers 2102.11968, arXiv.org, revised Mar 2022.
    13. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2021. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," JRFM, MDPI, vol. 14(3), pages 1-19, February.
    14. Jirô Akahori & Takafumi Amaba & Kaori Okuma, 2017. "A Discrete-Time Clark–Ocone Formula and its Application to an Error Analysis," Journal of Theoretical Probability, Springer, vol. 30(3), pages 932-960, September.
    15. Tsubasa Nishimura & Kenji Yasutomi & Tomooki Yuasa, 2022. "Higher-Order Error Estimates of the Discrete-Time Clark–Ocone Formula," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2518-2539, December.
    16. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    17. Mika Hujo, 2006. "Is the Approximation Rate for European Pay-offs in the Black–Scholes Model Always 1/ $$\sqrt{n}$$," Journal of Theoretical Probability, Springer, vol. 19(1), pages 190-203, January.
    18. Maria Elvira Mancino & Simona Sanfelici, 2020. "Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks," Risks, MDPI, vol. 8(4), pages 1-17, November.
    19. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    20. Johannes Ruf & Weiguan Wang, 2020. "Hedging with Linear Regressions and Neural Networks," Papers 2004.08891, arXiv.org, revised Jun 2021.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1004.4526. 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.