Option pricing in the presence of extreme fluctuations

15 January 1997

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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.

Authors

Didier Sornette , Marc Potters , Jean-Philippe Bouchaud