Information Theory and the Pricing of Contingent Claims: An Alternative Derivation of the Black–Scholes–Merton Formula

Abstract

This paper seeks to determine the best subjective probability to use to carry out expectation values of uncertain future cash flows with the smallest number of assumptions. This results in the unique distribution that guarantees no more information is present other than the stated assumptions. The result is a novel derivation of the well-known Black–Scholes equation without the need to introduce high-level mathematical machinery. This formalism fits nicely into introductory courses of finance, where the value of any financial instrument is given by the present value of uncertain future cash flows.