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

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  • Walter Schachermayer
  • Josef Teichmann

Abstract

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.

Suggested Citation

  • Walter Schachermayer & Josef Teichmann, 2007. "How close are the option pricing formulas of Bachelier and Black-Merton-Scholes?," Papers 0711.1272, arXiv.org.
    • Handle: RePEc:arx:papers:0711.1272
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    References listed on IDEAS

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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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    Cited by:

    1. René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2012. "A probabilistic numerical method for optimal multiple switching problems in high dimension," Working Papers hal-00747229, HAL.
    2. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    3. Ren'e Aid & Luciano Campi & Nicolas Langren'e & Huy^en Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Papers 1210.8175, arXiv.org.

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