Back to the Seventies: How a Free Lunch Falsifies the Black-Scholes Option Pricing Formula

Abstract

We show that the option pricing formula of Black and Scholes (1973) implies that a free lunch exists. Specifically, a risk-free profit can be made with zero investment, by trading call spreads in a simple economy where stock prices follow geometric Brownian motions. The option pricing formula must therefore be incorrect. We reconcile this upsetting finding with the theoretical literature by showing that, despite multiple attempts, the formula was never formally proven. Instead, and contrary to public belief, the formula was essentially an assumed result that over time became embedded in an increasingly refined mathematical framework.

Keywords: Black-Scholes-Merton option pricing, free lunch, circular reasoning