Digital contracts: Simple tools for pricing complex derivatives

This article presents a simple, unified approach for valuing a variety of financial assets using digital contracts. Three types of digitals are used: a digital option paying either one dollar or nothing, a digital share paying nothing or converting into one share of the underlying asset; and a first-touch digital paying one dollar the first time that the price of the underlying stock moves into some specified region. It is shown how the values of these three types of digitals can be determined for a wide variety of payoff events and how they can be combined to price complex contracts.