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Back to basics: historical option pricing revisited


  • Jean-Philippe Bouchaud

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

  • Marc Potters

    (Science & Finance, Capital Fund Management)


We 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.

Suggested Citation

  • Jean-Philippe Bouchaud & Marc Potters, 1998. "Back to basics: historical option pricing revisited," Science & Finance (CFM) working paper archive 500036, Science & Finance, Capital Fund Management.
  • Handle: RePEc:sfi:sfiwpa:500036

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Jean-Philippe Bouchaud, 1998. "Elements for a theory of financial risks," Science & Finance (CFM) working paper archive 500042, Science & Finance, Capital Fund Management.
    4. 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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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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