The two best ways to derive the Black–Scholes PDE

Abstract

PurposeThe purpose of this paper is to explain the Black–Scholes model with minimal technical requirements and to illustrate its impact from a business perspective.Design/methodology/approachThe paper employs simple accounting concepts and an argument part based on business need.FindingsThe Black–Scholes partial differential equation can be derived in many ways, some easy to understand, some hard, some useful and others not. The two methods in this paper are extremely insightful.Originality/valueThe paper takes a big-picture view of derivatives valuation. As such, it is a simple accompaniment to more complex methods and aims to keep modelling grounded in reality.