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

Walter Schachermayer; Josef Teichmann

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arXiv · 0711.1272

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

Walter Schachermayer·Josef Teichmann

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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.

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Walter Schachermayer, Josef Teichmann. 2007-11-08. How close are the option pricing formulas of Bachelier and Black-Merton-Scholes?. https://arxiv.org/abs/0711.1272

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