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

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. © 2008 The Authors. Journal compilation © 2008 Blackwell Publishing Inc.