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

2007/11/08 by Schachermayer, Walter, Teichmann, Josef · 1 citation
#FOS: Economics and business #FOS: Mathematics #History and Overview (math.HO) #Pricing of Securities (q-fin.PR) #Probability (math.PR)

paper · doi:10.48550/arxiv.0711.1272

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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• Path-dependent, ESG-valued, option pricing in the Bachelier-Black-Scholes-Merton model

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