Put-Call Parity and the Law
USC Working Paper No. 94-12
Posted: 10 Oct 1998
A common literary theme is the conflict between appearance and reality. That conflict also frequently arises in the law, where it is usually cast as one between substance and form. Another discipline in which the conflict arises is finance, where it appears in the put-call parity theorem. That theorem states that given any three of the four following financial instruments--a riskless zero-coupon bond, a share of stock, a call option on the stock, and a put option on the stock--the fourth instrument can be replicated. Thus, the theorem implies that any financial position containing these assets can be constructed in at least two different ways. Its legal significance arises when economically equivalent holdings receive different legal treatments because they are constructed from different instruments.That difficult legal issues are raised by the explosion of financial instruments, which places pressure on the existing but inconsistent legal categories, is well recognized in both the legal and finance literatures. This phenomenon, however, is not new, as is widely believed. These recent developments represent a difference in degree, not kind, with earlier developments. Using the put-call parity theorem, this paper describes how the ability to convert financial positions between stock, debt and options has long been used to circumvent legal rules. In addition, its application is not limited to financial instruments, because the theorem not only applies to market-traded debt, options and stocks, but to all financial positions that have cash flow patterns that correspond to these instruments. The paper traces the use of the put-call parity theorem to evade regulations that focus on form not substance back to Medieval England and the forerunner of the modern mortgage. The paper also discusses the significance of the put-call parity theorem for regulation more generally. It argues that the put-call parity theorem increases the intensity of regulatory competition and that the theorem undermines the tax law's distinction between owners and other interest holders.
JEL Classification: K19
Suggested Citation: Suggested Citation