Lognormal option pricing for arbitrary underlying assets: a synthesis

Abstract

All European option pricing formulas sharing the assumption of a lognormally distributed terminal price for the underlying asset are formally similar. It is thus natural to seek a single explicit general formula for this class of options. This paper provides such a synthesis. The key insight is recognizing that all option pricing equations depend explicitly on the expected terminal price of the arbitrary underlying asset, which is often obtained through basic financial reasoning. To illustrate the power and pedagogical value of this framework, I obtain several classical option pricing formulas as special cases of the general equation.