The Peculiar Logic of the Black-Scholes Model

The Black-Scholes(-Merton) model of options pricing establishes a theoretical relationship between the fair price of an option and other parameters characterizing the option and prevailing market conditions. Here I discuss a common application of the model with the following striking feature: the (expected) output of analysis apparently contradicts one of the core assumptions of the model on which the analysis is based. I will present several attitudes one might take toward this situation and argue that it reveals ways in which a broken model can nonetheless provide useful (and tradeable) information.