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Hedging Options with Scale-Invariant Models

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Author Info

  • Carol Alexander

    ()
    (ICMA Centre, University of Reading)

  • Leonardo M. Nogueira

    ()
    (ICMA Centre, University of Reading)

Abstract

A price process is scale-invariant if and only if the returns distribution is independent of the price level. We show that scale invariance preserves the homogeneity of a pay-off function throughout the life of the claim and hence prove that standard price hedge ratios for a wide class of contingent claims are model-free. Since options on traded assets are normally priced using some form of scale-invariant process, e.g. a stochastic volatility, jump diffusion or Lévy process, this result has important implications for the hedging literature. However, standard price hedge ratios are not always the optimal hedge ratios to use in a delta or delta-gamma hedge strategy; in fact we recommend the use of minimum variance hedge ratios for scale-invariant models. Our theoretical results are supported by an empirical study that compares the hedging performance of various smile-consistent scale-invariant and non-scale-invariant models. We find no significant difference between the minimum variance hedges in the smile-consistent models but a significant improvement upon the standard, model-free hedge ratios

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Bibliographic Info

Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2006-03.

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Length: 33 Pages
Date of creation: Jun 2006
Date of revision:
Publication status: Forthcoming in Journal of Banking and Finance
Handle: RePEc:rdg:icmadp:icma-dp2006-03

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Postal: PO Box 218, Whiteknights, Reading, Berks, RG6 6AA
Phone: +44 (0) 118 378 8226
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Web page: http://www.henley.reading.ac.uk/
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Related research

Keywords: Scale invariance; hedging; minimum variance; hedging; stochastic volatility;

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References

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  1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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  9. Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
  10. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
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  16. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
  17. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
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Cited by:
  1. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer, vol. 31(1), pages 13-32, May.

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