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