What is it?
- An option where the payoff is either some fixed amount of some asset, or nothing at all (discontinuous payoffs). The most common examples of binary options are the cash-or nothing and the asset-or-nothing options. Also called digital options.
How is it constructed?
- Binary options can either be European or American and be structured as a put or a call.
- Underlying asset can be an event or a price point being attained.
- If at maturity the binary expires in the money:
- Cash-or-nothing: buyer receives a predefined cash amount
- Asset-or-nothing: buyer receives an amount equal to the asset price itself.
- If instead it is out of the money, the option expires worthless.
Payout = C if ST > K = 0 if ST ≤ K
Where:
ST = spot price at maturity
K = strike price
C = pre-defined cash amount if it’s a cash or nothing option, and asset price in the case it’s an asset or nothing option
Max profit: Pre-agreed cash amount or the asset price at maturity
Max loss: Premium
When is it used?
- It is appropriate for an investor who believes that the market will be above/below a certain level at some specified time, but is not sure of the magnitude.
- Often is used to construct more complex option products.
- It can be seen as building blocks for a plain vanilla call which is constructed from an asset-or- nothing call with a short cash-or-nothing call where the cash payoff equals the strike.
What are the benefits?
- Less risky than traditional options as profits locked in as underlying performs, however, more expensive than a normal option.
- No need to constantly watch the underlying market level.
The Financial Engineer 
Binary options genarly a help for every one who wnat to deal in some fixed amount of some asset, or nothing at all. so each and every one want to a fixed price.
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