A digital option (also a binary option) is an option which pays off a fixed amount of money if a price or rate breaches a specific strike level. A range option is a compound version of a digital option where the underlying price or rate has to breach one level but not break through another level whether from downside or upside. That is, it has to end up within a predefined range. In essence, a range option is constructed using digital calls (binary calls) and digital puts (binary puts) with the same payoff. The payoff depends on whether the underlying remains within the range or not:

Range option = {Long lower boundary – digital call, short upper boundary- digital call}

Practically, digital options can be used to generate more sophisticated range structures. These types of options are particularly popular in commodity, FX, and interest rate markets. For example, in interest rate markets, they are usually packaged into cap- or floor-like serial forms having the short-term LIBOR rates as the underlyings, and with range levels changing or resetting period to period.