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Tracking Errors From Discrete Hedging In Exponential Lévy Models

  • MATS BRODÉN

    ()

    (Centre for Mathematical Sciences, Lund University, 22100 Lund, Sweden)

  • PETER TANKOV

    ()

    (Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France)

We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Lévy 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 Lévy process, and we give an explicit relation between the rate and the Blumenthal-Getoor index of the process.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 14 (2011)
Issue (Month): 06 ()
Pages: 803-837

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Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:06:p:803-837
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  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. Ale\v{s} \v{C}ern\'y & Jan Kallsen, 2007. "On the structure of general mean-variance hedging strategies," Papers 0708.1715, arXiv.org.
  3. 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.
  4. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
  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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