Option contract with an all-or-nothing payoff based on whether a specified market condition is satisfied.
A binary option is an option contract whose payoff depends on a yes-or-no condition. If the condition is satisfied, the holder receives a fixed payout. If it is not satisfied, the holder receives nothing.
Unlike a standard call or put, a binary option does not give the holder the right to buy or sell the underlying asset. The payoff is a fixed cash amount or zero.
The payoff shape is a step, not a smooth line. Once the condition is met at the relevant measurement time, the payout jumps to the fixed amount.
For a simple cash-or-nothing binary call measured at expiration:
where \(Q\) is the fixed payout, \(S_T\) is the underlying price at expiration, and \(K\) is the trigger level.
| Structure | Trigger | Practical point |
|---|---|---|
| Cash-or-nothing binary call | Underlying finishes above a level | Fixed cash payout, no asset delivery |
| Cash-or-nothing binary put | Underlying finishes below a level | Fixed cash payout if downside condition is met |
| One-touch option | Underlying touches a level before expiration | Path-dependent trigger |
| No-touch option | Underlying does not touch a level | Risk is whether the barrier is avoided |
The exact contract language controls whether the condition is measured at expiration, continuously, intraday, at official settlement, or through another reference source.
Suppose a binary option costs $40 and pays $100 if an index closes above 5,000 on the expiration date.
5,010, the holder receives $100, for a $60 gross gain before costs.4,999, the holder receives nothing and loses the $40 paid.The difference between a small win and a total loss can be one tick around the reference level.
Binary options are useful for understanding digital payoff risk, event contracts, structured products, and some exotic OTC options. They can also be dangerous when marketed as simple short-term bets.
The main analytical issues are:
Do not confuse a binary option with an ordinary call or put. A standard call gains more value as the underlying rises above the strike. A binary option usually pays the same fixed amount once the condition is satisfied.
Before trading or analyzing a binary option, verify: