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How close are the option pricing formulas of Bachelier and Black-Merton-Scholes?

  • Walter Schachermayer
  • Josef Teichmann
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    We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to obtain applicable formulas for option pricing in pre-computer time. Furthermore we explain -- by simple methods from chaos expansion -- why Bachelier's model yields good short-time approximations of prices and volatilities.

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    File URL: http://arxiv.org/pdf/0711.1272
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    Paper provided by arXiv.org in its series Papers with number 0711.1272.

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    Date of creation: Nov 2007
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    Handle: RePEc:arx:papers:0711.1272
    Contact details of provider: Web page: http://arxiv.org/

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    1. Boyle, Phelim P. & Ananthanarayanan, A. L., 1977. "The impact of variance estimation in option valuation models," Journal of Financial Economics, Elsevier, vol. 5(3), pages 375-387, December.
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