The Quintessential Option Pricing Formula

Max Skipper and Peter Buchen

Abstract

It might be argued that nothing more can be said about pricing options under the Black-Scholes paradigm. We express the opposite view by presenting in this paper a new formula that unifies much of the existing literature on pricing exotic options within the Black-Scholes framework. The formula gives the arbitrage-free price of an M-binary (a generalised multi-asset, multi-period binary option), which is a fundamental building block for more complex exotic options. To demonstrate the utility of the formula, we apply it to pricing several well known exotics and also to a new option: a discretely monitored call barrier option on the maximum of several assets.

Keywords: Exotic options, binaries, digitals, static replication.