A binary option is a financial exotic option in which the payoff is either some fixed monetary amount or nothing at all.^[1][2] The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The former pays some fixed amount of cash if the option expires in-the-money while the latter pays the value of the underlying security. They are also called all-or-nothing options, digital options (more common in forex/interest rate markets), and fixed return options (FROs) (on the NYSE American).^[3]

While binary options may be used in theoretical asset pricing, they are prone to fraud in their applications and hence banned by regulators in many jurisdictions as a form of gambling.^[4] Many binary option outlets have been exposed as fraudulent.^[5] The U.S. FBI is investigating binary option scams throughout the world, and the Israeli police have tied the industry to criminal syndicates.^[6][7][8] The European Securities and Markets Authority (ESMA) has banned retail binary options trading.^[9] Australian Securities & Investments Commission (ASIC) considers binary options as a "high-risk" and "unpredictable" investment option, ^[10] and finally also banned binary options sale to retail investors in 2021.^[11]

The FBI estimates that the scammers steal US$10 billion annually worldwide.^[12] The use of the names of famous and respectable people such as Richard Branson to encourage people to buy fake "investments" is frequent and increasing.^[13] Articles published in The Times of Israel newspaper explain the fraud in detail, using the experience of former insiders such as a job-seeker recruited by a fake binary options broker, who was told to "leave conscience at the door".^[14][15] Following an investigation by The Times of Israel, Israel's cabinet approved a ban on the sale of binary options in June 2017,^[16] and a law banning the products was approved by the Knesset in October 2017.^[17][18]

On January 30, 2018, Facebook banned advertisements for binary options trading as well as for cryptocurrencies and initial coin offerings (ICOs).^[19][20] Google and Twitter announced similar bans in the following weeks.^[21]

Function

Binary options "are based on a simple 'yes' or 'no' proposition: Will an underlying asset be above a certain price at a certain time?"^[22] Traders place wagers as to whether that will or will not happen. If a customer believes the price of an underlying asset will be above a certain price at a set time, the trader buys the binary option, but if he or she believes it will be below that price, they sell the option. In the U.S. exchanges, the price of a binary is always under $100.^[22]

Investopedia described the binary options trading process in the U.S. thus:

binary may be trading at $42.50 (bid) and $44.50 (offer) at 1 p.m. If you buy the binary option right then you will pay $44.50, if you decide to sell right then you'll sell at $42.50.

Let's assume you decide to buy at $44.50. If at 1:30 p.m. the price of gold is above $1,250, your option expires and it becomes worth $100. You make a profit of $100 – $44.50 = $55.50 (less fees). This is called being "in the money".

But if the price of gold is below $1,250 at 1:30 p.m., the option expires at $0. Therefore you lose the $44.50 invested. This is called being "out of the money".

The bid and offer fluctuate until the option expires. You can close your position at any time before expiry to lock in a profit or a reduce a loss (compared to letting it expire out of the money).^[22]

In the U.S., every binary option settles at $100 or $0, $100 if the bet is correct, 0 if it is not.^[22]

In the online binary options industry, where the contracts are sold by a broker to a customer in an OTC manner, a different option pricing model is used. Brokers sell binary options at a fixed price (e.g., $100) and offer some fixed percentage return in case of in-the-money settlement. Some brokers, also offer a sort of out-of-money reward to a losing customer. For example, with a win reward of 80%, out-of-money reward of 5%, and the option price of $100, two scenarios are possible. In-the-money settlement pays back the option price of $100 and the reward of $80. In case of loss, the option price is not returned but the out-of-money reward of $5 is granted to the customer.^[23]

On non-regulated platforms, client money is not necessarily kept in a trust account, as required by government financial regulation, and transactions are not monitored by third parties in order to ensure fair play.^[24]

Binary options are often considered a form of gambling rather than investment because of their negative cumulative payout (the brokers have an edge over the investor) and because they are advertised as requiring little or no knowledge of the markets. Gordon Pape, writing in Forbes.com in 2010, called binary options websites "gambling sites, pure and simple", and said "this sort of thing can quickly become addictive... no one, no matter how knowledgeable, can consistently predict what a stock or commodity will do within a short time frame".^[25]

Pape observed that binary options are poor from a gambling standpoint as well because of the excessive "house edge". One online binary options site paid $71 for each successful $100 trade. "If you lose, you get back $15. Let's say you make 1,000 "trades" and win 545 of them. Your profit is $38,695. But your 455 losses will cost you $38,675. In other words, you must win 54.5% of the time just to break even".^[25]

The U.S. Commodity Futures Trading Commission warns that "some binary options Internet-based trading platforms may overstate the average return on investment by advertising a higher average return on investment than a customer should expect given the payout structure."^[26]

Black–Scholes valuation

In the Black–Scholes model, the price of the option can be found by the formulas below.^[27] In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put – the binary options are easier to analyze, and correspond to the two terms in the Black–Scholes formula.

In these, S is the initial stock price, K denotes the strike price, T is the time to maturity, q is the dividend rate, r is the risk-free interest rate and ${\displaystyle \sigma }$ is the volatility. ${\displaystyle \Phi }$ denotes the cumulative distribution function of the normal distribution,

${\displaystyle \Phi (x)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{x}e^{-z^{2}/2}dz.}$

and,

${\displaystyle d_{1}={\frac {\ln {\frac {S}{K}}+(r-q+\sigma ^{2}/2)T}{\sigma {\sqrt {T}}}}.}$

${\displaystyle d_{2}=d_{1}-\sigma {\sqrt {T}}.}$

Cash-or-nothing call

This pays out one unit of cash if the spot is above the strike at maturity. Its value now is given by

${\displaystyle C=e^{-rT}\Phi (d_{2}).\,}$

Cash-or-nothing put

This pays out one unit of cash if the spot is below the strike at maturity. Its value now is given by

${\displaystyle P=e^{-rT}\Phi (-d_{2}).\,}$

Asset-or-nothing call

This pays out one unit of asset if the spot is above the strike at maturity. Its value now is given by

${\displaystyle C=Se^{-qT}\Phi (d_{1}).\,}$

Asset-or-nothing put

This pays out one unit of asset if the spot is below the strike at maturity. Its value now is given by:

${\displaystyle P=Se^{-qT}\Phi (-d_{1}).\,}$

American style

An American option gives the holder the right to exercise at any point up to and including the expiry time ${\displaystyle T}$. That is, denoting by ${\displaystyle K}$ the strike price, if ${\displaystyle K\geq S}$ (resp. ${\displaystyle K\leq S}$), the corresponding American binary put (resp. call) is worth exactly one unit. Let

${\displaystyle a={\frac {1}{\sigma }}\ln(K/S){\text{, }}\xi ={\frac {r-q}{\sigma }}-{\frac {\sigma }{2}}{\text{, and }}b={\sqrt {\xi ^{2}+2r}}.\,}$

The price of a cash-or-nothing American binary put (resp. call) with strike ${\displaystyle K<S}$ (resp. ${\displaystyle K>S}$) and time-to-expiry ${\displaystyle T}$ is:

${\displaystyle \frac{1}{2}{e}^{a\left(\mathrm{\xi <!--\; \xi \; -->}-<!--\; -\; -->b\right)}\{1+\mathrm{sgn}<!--\; \; -->(a)\mathrm{erf}<!--\; \; -->\left(\frac{bT-<!--\; -\; -->a}{\sqrt{2T}}\right)+e^{2ab}}$Zdroj:https://en.wikipedia.org?pojem=Binary_option
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