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Tracking Errors From Discrete Hedging In Exponential Lévy Models

Author

Listed:
  • MATS BRODÉN

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

  • PETER TANKOV

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

Abstract

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.

Suggested Citation

  • Mats Brodén & Peter Tankov, 2011. "Tracking Errors From Discrete Hedging In Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 803-837.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:06:n:s0219024911006760
    DOI: 10.1142/S0219024911006760
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    Keywords

    Exponential Lévy models; quadratic hedging; delta hedging; discretization error; L2 convergence; digital options;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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