Binary Or Digital Option

Binary option
Definition: A binary option is a type of option where there are only two possible outcomes - the payoff is either some fixed amount of asset or nothing at all.

Types: (1) The cash-or-nothing binary option pays some fixed amount of cash if the option expires in-the-money. (2) The asset-or-nothing pays the value of the underlying security.

Other Names: They are also called all-or-nothing options, digital options, or Fixed Return Options (FROs).

Expiration Values for a European:

exhibits

American vs European: Binary options are usually European-style – for a call, the price of the underlying must be above the strike at the expiration date. American binary options exist also, but these automatically exercise whenever the price “touches” the strike price, yielding very different behaviour.

Exchange-traded binary options: Binary option contracts have long been available Over-the-counter i.e. sold directly by the issuer to the buyer. They were generally considered "exotic" instruments and there was no liquid market for trading these instruments between their issuance and expiration. They were often seen embedded in more complex option contracts.

Standardization:
- Options Clearing Corporation allowed binary options………………2007
- Securities and Exchange Commission approved cash-or-nothing binary options…………………2008
- American Stock Exchange launched exchange-traded European cash-or-nothing binary options..5/2008
- Chicago Board Options Exchange (CBOE) followed………6/2008

Constraints (to reduce risk of single stock manipulation):
- Amex FROs use a "settlement index" defined as a volume-weighted average of trades on the expiration day.
- The American Stock Exchange and Donato A. Montanaro (CEO of online brokerage) use a volume-weighted settlement index for exchange-listed binary options.
- You can sell your contract back to the market maker before it expires, if you see the underlier value going higher and there is a reducing possibility of winning the trade. However, the present price of the contract is recalculated considering the current situation on the markets.

Black-Scholes Valuation
Equation

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