A 50-year Retrospect of the Black-Scholes-Merton (BSM) Argument through Three Questions

Abstract

This paper provides a retrospect of the Black-Scholes-Merton (BSM) argument that is used to derive the common BSM formula. The paper utilizes and builds upon a frame used to provide a retrospect of the Put-Call Parity (PCP) provided in Wurts (2018a). Accordingly, this paper fills a promise that lessons-learned from PCP analysis can be applied to more complex models for financial derivatives, and leads to a subsequent promise that lessons-learned from BSM analysis can also be applied to more-complex financial instruments and their models. The paper utilizes heuristics already developed for PCP analysis (as found in Wurts (2018a, 2018b, and 2019)) and introduces additional heuristics that can be useful in the corporate governance of model validation, including the micro corporate governance of financial instrument valuation models. The paper address three retrospect questions. (1) Should the BSM argument hold? (No.) (2) Has the BSM argument held? (Not necessarily.) (3) What are consequences for presuming the BSM argument has held? (Inconsistent logic, with added details.) The paper also provides an assessment regarding how other scholars have provided a different retrospect on the BSM model in general. And while other scholars have emphasized a naming of the BSM Formula (i.e., the seminal formula for a Call option) and the BSM Equation (i.e., the seminal fundamental partial differential equation for “all” derivatives, that leads to the BSM Formula), it is not clear that scholars have well characterized the BSM Argument. Hence, an introductory description of the BSM Argument is provided herein, in the context of what the BSM model and approach is.