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Tracking errors from discrete hedging in exponential L\'evy models

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  • Mats Brod'en
  • Peter Tankov

Abstract

We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice of delta hedging, and show that for discontinuous option pay-offs the latter strategy may suffer from very large discretization errors. For options with discontinuous pay-offs, the convergence rate depends on the underlying Levy process, and we give an explicit relation between the rate and the Blumenthal-Getoor index of the process.

Suggested Citation

  • Mats Brod'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709, arXiv.org.
  • Handle: RePEc:arx:papers:1003.0709
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    File URL: http://arxiv.org/pdf/1003.0709
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    References listed on IDEAS

    as
    1. 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.
    2. Alev{s} v{C}ern'y & Jan Kallsen, 2007. "On the Structure of General Mean-Variance Hedging Strategies," Papers 0708.1715, arXiv.org, revised Jul 2017.
    3. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    5. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
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    Cited by:

    1. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
    2. Thai Huu Nguyen & Serguei Pergamenschchikov, 2015. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Papers 1505.02627, arXiv.org.
    3. Mathieu Rosenbaum & Peter Tankov, 2011. "Asymptotically optimal discretization of hedging strategies with jumps," Papers 1108.5940, arXiv.org, revised Apr 2014.
    4. Huu Thai Nguyen & Serguei Pergamenchtchikov, 2014. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Working Papers hal-00979199, HAL.
    5. Stefan Geiss & Emmanuel Gobet, 2011. "Fractional smoothness and applications in Finance," Post-Print hal-00474803, HAL.
    6. 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.
    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.

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