Too Much Of A Good Thing? A Review Of Volatility Extensions In Black-Scholes

Abstract

Since the seminal Black and Scholes model was introduced in the 1970s, researchers and practitioners have been continuously developing new models to enhance the original. All these models aim to ease one or more of the Black and Scholes assumptions, but this often results in a set of equations that is difficult if not impossible to use in practice. Nevertheless, in the wake of the financial crisis, an understanding of the various pricing models is essential to calm investors’ nerves. This paper reviews the models developed since Black and Scholes, giving the advantages and disadvantages of each type. It focuses on the main variable for which Black and Scholes gives results that differ widely from market data: implied volatility. This variable also forms the basis for the development of a new type of models, called “market models.”