Option Pricing Model: Comparing Louis Bachelier with Black-Scholes Merton

Abstract

The paper reviews the option pricing model constructs of Bachelier and Black-Scholes Merton, concluding the latter model approximates the former. The paper demonstrates that certain critiques of the Bachelier model outlined in the 1960s and 1970s are not sound; and Bachelier’s model can be readily adapted to the modern markets, contracts and price path assumptions. Further the modern price path assumptions are analysed showing the log-normal distribution is poorly justified, and the risk free hedge justification is weak in a dynamic time setting. This resolves in the discount rate being the underlying risky asset return with a normal dispersal.

Keywords: Bachelier, Black-Scholes, Merton, Option Pricing

JEL Classification: G13