Back to basics: historical option pricing revisited
AbstractWe reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments are uncorrelated (but not necessarily independent) and of arbitrary probability density. We discuss in particular how, in the Gaussian limit, the Black-Scholes results are recovered, including the fact that the average return of the underlying stock disappears from the price (and the hedging strategy). We compare this theory to real option prices and find these reflect in a surprisingly accurate way the subtle statistical features of the underlying asset fluctuations.
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Bibliographic InfoPaper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500036.
Date of creation: Aug 1998
Date of revision:
Publication status: Published in Philosophical Transactions: Mathematical, Physical & Engineering Sciences 357, 2019 - 2028 (1999)
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)
- NEP-RMG-2005-02-13 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997.
"Scaling in stock market data: stable laws and beyond,"
- Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Science & Finance (CFM) working paper archive 9705087, Science & Finance, Capital Fund Management.
- Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
- Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1998. "Strings Attached," Science & Finance (CFM) working paper archive 500049, Science & Finance, Capital Fund Management.
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