Removing the 'Black Box' from the Black-Scholes Option Pricing Model

Abstract

In The Ascent of Money (2008), the Harvard financial historian Niall Ferguson refers to the Black-Scholes option pricing model 'as a black box' which is beyond comprehension of anyone except the mathematically astute and leaves most investors baffled. In this paper, we develop a heuristic proof of Black-Scholes as an aid to learning, discovery and problem solving. From a deterministic model, the basic structure of Black-Scholes is identified. Thereafter, the generalized form of Black-Scholes is deduced and various underlying components examined with particular emphasis on a conceptual understanding of the symbols N(d1) and N(d2). The methodology relies heavily on intuition and transparency with the more rigorous mathematics relegated to the appendices.