About Binary Options

Binary options behave similarly to standard options, but the payout is based on whether the option is on the money, not by how much it is in the money. For this reason they are also called all-or-nothing options.

As with a standard European style option, the payoff is based on the price of the underlying asset on the expiration date. Unlike with standard options, the payoff is fixed at the writing of the contract. Binary options may incorporate barrier features, which are as described in the Barrier Functions section:

1) Down and Out

The option is canceled or knocked-out if the asset falls to a predetermined boundary price.

2) Down and In

The option is activated or knocked-in if the asset falls to a predetermined boundary price.

3) Up and Out

The option is canceled or knocked-out if the asset rises to a predetermined boundary price.

4) Up and In

The option is activated or knocked-in if the asset rises to a predetermined boundary price.

Benefits

The purchaser and writer of binary options need only determine an expected direction of price movement, rather the direction and the magnitude, in order to effectively use the option.

Features

The payout profile (and hence sensitivity to price changes) of binary options is discontinuous.

The cash payoff may be equal to the strike price, or it may be greater or less, in which case the option is a gap option.

Intrinsic Value Formula

The payoff at expiration is:

Call: 0, if U < K; X, if U > K

Put: 0, if U > K, X, if U < K

where U is the underlying price, E is the exercise or strike price, and X is the payoff for a cash-or-nothing, or U, for an asset-or-nothing option; additional condition is that D&O and U&O binary barriers are worth R or rebate if barrier is reached.

Aliases

Binary options are also known as digital options and all-or-nothing options.

Uses

1) A bank wishes to hedge a key interest rate exceeding a certain level. It purchases a binary option with strike at the level at which they wish to hedge. If the interest rate exceeds that level, they receive a fixed payment, no matter how high the rate goes.