Recent Developments in Options Theory: From Black-Scholes to Market Models

Abstract

Since the seminal Black-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-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-Scholes, giving the advantages and disadvantages of each type. It focuses on the two main variables for which Black-Scholes gives results that differ widely from market data: implied volatility and risk-neutral density. These variables also form the basis for the development of a new type of models, called “market models”.