How close are the option pricing formulas of bachelier and black-merton-scholes?

  • Schachermayer W
  • Teichmann J
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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.

Author-supplied keywords

  • Bachelier formula
  • Black-Merton-Scholes formula
  • No arbitrage
  • Short time asymptotics

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Authors

  • Walter Schachermayer

  • Josef Teichmann

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