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Option pricing in the presence of extreme fluctuations

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  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Didier Sornette

    (UCLA
    Science & Finance, Capital Fund Management)

  • Marc Potters

    (Science & Finance, Capital Fund Management)

Abstract

We discuss recent evidence that B. Mandelbrot's proposal to model market fluctuations as a Lévy stable process is adequate for short enough time scales, crossing over to a Brownian walk for larger time scales. We show how the reasoning of Black and Scholes should be extended to price and hedge options in the presence of these `extreme' fluctuations. A comparison between theoretical and experimental option prices is also given.

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Bibliographic Info

Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500038.

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Date of creation: Jan 1997
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Publication status: Published in `Mathematics of derivative securities', M. Dempster and S. Pliska Edts, Cambridge University Press, Cambridge UK (1997)
Handle: RePEc:sfi:sfiwpa:500038

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Cited by:
  1. Jean-Philippe Bouchaud & Didier Sornette & Christian Walter & Jean-Pierre Aguilar, 1998. "Taming large events: portfolio selection for strongly fluctuating assets," Science & Finance (CFM) working paper archive 500044, Science & Finance, Capital Fund Management.
  2. A. Johansen & D. Sornette, 1997. "Stock market crashes are outliers," Papers cond-mat/9712005, arXiv.org, revised Dec 1997.

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