A 50-Year Retrospect of the Put-Call Parity (PCP) Through Three Questions

Abstract

A half-century retrospect of Stoll (1969) provides lessons to be learned from the Put-Call Parity (PCP) and its applications. Many of the lessons are generalizable to models for risk assessment, valuation, and exposure that have been developed for more-complex financial derivatives. Yet since the PCP is a simple algebraic model of financial derivatives, it is a model that is likely assessable to all and allows the analysis focus to shift from assessing complex mathematics to assessing economic issues surrounding financial derivatives. Indeed, aspects of narrow financial crises such as Enron in 2001 as well as broad financial crises such as in 2007 can be assessed regarding how the PCP can be generalized to more-complex financial derivatives — aspects of those crises find bearing in how the PCP has been misapplied. This paper highlights and demonstrates two important misapplications of the PCP: (1) a narrow application, i.e., the presumption that the PCP can provide what can be characterized as a “missing price,” even for a stand-alone financial instrument, and (2) a broader application that also applies to the narrow one, i.e., the presumption that the PCP always “holds” — that is, holds prices in a strict relationship characterized by an economic price-parity model based on mathematical payouts of the financial instruments. A bright-line test is introduced, to help assess whether the PCP has been applied correctly, and the test helps identify the distinction between three related Put-Call Concepts: Put-Call Equivalency of mathematical payouts (PCE), Put-Call Valuation of economic payouts (PCV), and the Put-Call Parity of prices (i.e., PCP). The analysis herein is multi-disciplinary, which highlights the versatility and usefulness of the PCP as an archetypal financial derivatives model; consequently, an analysis of the PCP can push forward research threads in a diversity of academic disciplines outside finance, including legal argument, rhetorical analysis, and applications of the creativity process in other business disciplines. Accordingly, the PCP can be explored through at least three questions: has it held, should it always hold, and how powerful is a formal argument that erroneously assumes it should hold for a specific application? Addendum is available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3758189 Bibliography is available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3758188