HOW CLOSE ARE THE OPTION PRICING FORMULAS OF BACHELIER AND BLACK–MERTON–SCHOLES?

Walter Schachermayer and Josef Teichmann

Mathematical Finance, 2008, vol. 18, issue 1, 155-170

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.

Date: 2008
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https://doi.org/10.1111/j.1467-9965.2007.00326.x

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