The Progress of Black-Scholes Model and Black-Scholes-Merton Model

Abstract

Black-Scholes (BS) model was first proposed in 1973, which has been modified by Robert Merton as the Black-Scholes-Merton (BSM) model subsequently. Contemporarily, these two models have been widely used and praised by financial scholars as well as employees. Plenty of scholars have tried to verify the accuracy of the and expressed their views on the existing defects in above models. Based on the existing literature, this article first introduces and derives the two models step by step and discusses the basic assumptions for these models. Subsequently, the applications of the two models are demonstrated separately. Specifically, the project valuation based on BS model is presented detaily while the applications of BSM model are introduced from four aspects (pricing of intangible assets, risk avoidance, default prediction and employee stock option’s pricing). Afterwards, the limitations and gaps of the models (e.g., volatility smile) ascribed to the ideal assumptions are discussed. In order to tackle the issue, improvement and suggestions are proposed including extending the models with different forms. These results offer a guideline for the option pricing, which can be widely applied in investment strategy.