Smiling At Black-Scholes

The existence of the volatility smile is a tremendous validation of the real-life usefulness of the Black-Scholes model. It very clearly explains why practitioners have embraced and continue to embrace the model, in spite of its wide-off-the-mark mathematical foundations (in particular, the assumption that asset prices are lognormally distributed). Derivatives players don´t trust “pure” results from Black-Scholes but they will continue using the model because they can so easily fix it into delivering the results that they, and not some unrealistic theoretical device, deem appropriate. The smile very graphically shows how easily, in fact.

Black-Scholes comes with a built-in self-correcting mechanism that very conveniently lets traders manipulate the model so as to freely express their opinions and obtain the prices that are considered optimal from a practical point of view. This freedom-providing feature (which works by fudging the volatility parameter that goes into the formula) is the number one reason behind the spectacular real-life success of the model. The volatility smile, by reflecting those freely-expressed opinions and how Black-Scholes permits users to break free from its own mathematical straightjacket, symbolizes such success.

The smile is saying both things at the same time: “Black-Scholes is wrong, but it is right!”. The model is mathematically wrong, but it can be righted through its built-in self-correction mechanism. By easily making mathematics irrelevant, the model gained a prominent place in the hearts of traders (who are only too aware of the limitations of mathematical modelling when it comes to the financial markets).