Option pricing in the presence of extreme fluctuations
AbstractWe 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 InfoPaper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500038.
Date of creation: Jan 1997
Date of revision:
Publication status: Published in `Mathematics of derivative securities', M. Dempster and S. Pliska Edts, Cambridge University Press, Cambridge UK (1997)
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-13 (All new papers)
- NEP-CFN-2005-02-13 (Corporate Finance)
- NEP-FIN-2005-02-13 (Finance)
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- A. Johansen & D. Sornette, 1997. "Stock market crashes are outliers," Papers cond-mat/9712005, arXiv.org, revised Dec 1997.
- 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.
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