# Binary option

A binary option is a financial option in which the payoff is either some fixed monetary amount or nothing at all. While binary options are used in a theoretical framework as the building block for asset pricing and financial derivatives (a binary option maps to the cumulative distribution function of the risk-neutral distribution [1][2]), they have been exploited by fraudulent operations as many binary option outlets (outside regulated markets) have been shown to be scams. The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The cash-or-nothing binary option pays some fixed amount of cash if the option expires in-the-money while the asset-or-nothing 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 American Stock Exchange).[3]

Though binary options sometimes trade on regulated exchanges, they are generally unregulated, trading on the internet, and prone to fraud.[3] The U.S. Securities and Exchange Commission (SEC) and Commodity Futures Trading Commission (CFTC) have issued a joint warning to American investors regarding unregulated binary options.[4] and have forced a major operator, Banc de Binary, to cease operations in the US and pay back all customer losses. Many binary option "brokers" have been exposed as questionable operations. With such binary option brokers, there is no real brokerage; the customer is betting against the broker, who is acting as a bucket shop. Manipulation of price data to cause customers to lose is common. Withdrawals are regularly stalled or refused by such operations.[5]

## Regulation and compliance

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.[6]

On May 3, 2012, the Cyprus Securities and Exchange Commission (CySEC) announced a policy change regarding the classification of binary options as financial instruments. The effect is that binary options platforms operating in Cyprus, where many of the platforms are now based, will have to be CySEC regulated within six months of the date of the announcement. CySEC was the first EU MiFID-member regulator to treat binary options as financial instruments.[7]

In March 2013, the Malta Financial Services Authority announced that binary options regulation would be transferred away from Malta's Lottery and Gaming Authority.[8] On 18 June 2013, Malta’s Financial Services Authority confirmed that in their view binary options fell under the scope of the Markets in Financial Instruments Directive (MiFID) 2004/39/EC. With this announcement Malta became the second EU jurisdiction to regulate binary options as a financial instrument; providers will now have to gain a category 3 Investment Services licence and conform to MiFID's minimum capital requirements.[9] Prior to this announcement it had been possible for firms to operate from the jurisdiction provided the firm had a valid Lottery and Gaming Authority licence.

In 2013, CySEC prevailed over the disreputable binary options brokers and communicated intensively with traders in order to prevent the risks of using unregulated financial services. On September 19, 2013, CySEC sent out a press release warning investors against binary options broker TraderXP; CySEC stated that TraderXP was not and had never been licensed by CySEC.[10] On October 18, 2013, CySEC released an investor warning about binary options broker NRGbinary and its parent company NRG Capital (CY) Ltd., stating that NRGbinary was not and had never been licensed by CySEC.[11]

The Cypriot regulator also temporarily suspended the license of the Cedar Finance on December 19, 2013. The decision was taken by CySEC because the potential violations referenced appeared to seriously endanger the interests of the company’s customers and the proper functioning of capital markets, as described in the official issued press release. CySEC also issued a warning against binary option broker PlanetOption at the end of the year and another warning against binary option broker LBinary on January 10, 2014, pointing out that it was not regulated by the Commission and the Commission had not received any notification by any of its counterparts in other European countries to the effect of this firm being a regulated provider.

As far as penalties are concerned, the Cyprus regulator imposed a penalty of €15,000 against ZoomTrader. OptionBravo and ChargeXP were also financially penalized. CySEC also indicated that it had voted to reject the ShortOption license application.[12]

The Australian Securities & Investments Commission (ASIC) warned Australian investors on Friday 13 February 2015 against Opteck, an unlicensed binary option provider.[13] The ASIC later began a focused effort to control unlicensed derivative providers, including "review" websites, broker affiliates and managed service providers related to binary option products.[14]

The U.S. Commodity Futures Trading Commission (CFTC) oversees the regulation of futures, options, and swaps trading in the United States. On June 6, 2013, the CFTC and the U.S. Securities and Exchange Commission jointly issued an Investor Alert to warn about fraudulent promotional schemes involving binary options and binary options trading platforms. At the same time they charged Israeli-Cypriot Banc De Binary Ltd., with illegally selling binary options to U.S. investors.[15][16] The company reached an $11 million settlement with U.S. Authorities.[17] In 2015, CySEC repeatedly fined Banc De Binary for several violations including the solicitation of US clients.[18][19] In 2016, the regulator fined Banc De Binary Ltd once again for violation of its legislation. The broker has come to a settlement of €350,000.[20] In July 2016, the Israeli binary option firms Vault Options, Ltd. and Global Trader 365 were ordered by the U.S. District Court of Northern Illinois to pay more than$4.5 million for unlawful off-exchange binary options trading, fraud, and registration violations. The companies were also banned permanently from operating in the US or selling to US residents.[21]

In November 2016, the Israel Securities Authority carried out a raid on the Ramat Gan offices of binary option broker iTrader. The CEO and six other employees were charged with fraud, providing unlicensed investment advice, and obstruction of justice.[22]

## Criticism

Further information: Securities fraud

These platforms may be considered by some as gaming or gambling platforms rather than investment platforms because of their negative cumulative payout (they have an edge over the investor) and because they require little or no knowledge of the stock market to trade. According to Gordon Pape, writing in Forbes, "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".[23]

The Times of Israel has run a series of articles, "The wolves of Tel Aviv: Israel's vast, amoral binary options scam exposed" exposing the industry as a scam.[5] In a second article, the Times describes in detail how an binary options salesman fleeced clients. "According to one ex-employee of a firm that employs over 1,000 people in a high-rise office building in Tel Aviv, losses are guaranteed because the 'dealing room' at the binary options firm controls the trading platform — like the crooked ownership of a rigged casino manipulating the roulette wheel." [24]

In August 2016, Belgium's Financial Services and Markets Authority banned binary options schemes, based on concerns about widespread fraudulent activity.[25]

In 2007, the Options Clearing Corporation proposed a rule change to allow binary options,[26] and the Securities and Exchange Commission approved listing cash-or-nothing binary options in 2008.[27] In May 2008, the American Stock Exchange (Amex) launched exchange-traded European cash-or-nothing binary options, and the Chicago Board Options Exchange (CBOE) followed in June 2008. The standardization of binary options allows them to be exchange-traded with continuous quotations.

Amex offers binary options on some ETFs and a few highly liquid equities such as Citigroup and Google. Amex calls binary options "Fixed Return Options" (FROs); calls are named "Finish High" and puts are named "Finish Low". To reduce the threat of market manipulation of single stocks, Amex FROs use a "settlement index" defined as a volume-weighted average of trades on the expiration day. Amex and Donato A. Montanaro submitted a patent application for exchange-listed binary options using a volume-weighted settlement index in 2005.[28]

CBOE offers binary options on the S&P 500 (SPX) and the CBOE Volatility Index (VIX).[29] The tickers for these are BSZ[30] and BVZ, respectively.[31] CBOE only offers calls, as binary put options are trivial to create synthetically from binary call options. BSZ strikes are at 5-point intervals and BVZ strikes are at 1-point intervals. The actual underlying to BSZ and BVZ are based on the opening prices of index basket members.

Both Amex and CBOE listed options have values between $0 and$1, with a multiplier of 100, and tick size of $0.01, and are cash settled.[29] In 2009, Nadex, a U.S.-based binary options provider launched binary options on a range of forex, commodities and stock indices markets.[32] ## Example of a binary options trade A trader who thinks that the EUR/USD price will close at or above 1.2500 at 3:00 p.m. can buy a call option on that outcome. A trader who thinks that the EUR/USD price will close at or below 1.2500 at 3:00 p.m. can buy a put option or sell a call option contract. At 2:00 p.m. the EUR/USD price is 1.2490. The trader believes this will increase, so he buys 10 call options for EUR/USD at or above 1.2500 at 3:00 p.m. at a cost of$40 each.

The risk involved in this trade is known. The trader’s gross profit/loss follows the "all or nothing" principle. He can lose all the money he invested, which in this case is $40 x 10 =$400, or receive $100 x 10 =$1,000. If the EUR/USD price will close at or above 1.2500 at 3:00 p.m. the trader's profit will be the payoff at expiry minus the cost of the option: $1,000 –$400 = $600. The trader can also choose to liquidate (buy or sell in order to close) his position prior to expiration, at which point the option value is not guaranteed to be$100. The larger the gap between the spot price and the strike price, the value of the option decreases, as the option is less likely to expire in the money.

In this example, at 3:00 p.m. the spot has risen to 1.2505. The option has expired in the money and the gross payoff is $1,000. The trader's net profit is$600.

## Black–Scholes valuation

In the Black–Scholes model, the price of the option can be found by the formulas below.[33] 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,

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

and,

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

### 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

American binary put with K = 100, r = 0.04, σ = 0.2, T = 1.

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 (resp. ${\displaystyle K>S}$) and time-to-expiry ${\displaystyle T}$ is

${\displaystyle {\frac {1}{2}}e^{a\left(\xi -b\right)}\left\{1+\operatorname {sgn} (a)\operatorname {erf} \left({\frac {bT-a}{\sqrt {2T}}}\right)+e^{2ab}\left[1-\operatorname {sgn} (a)\operatorname {erf} \left({\frac {bT+a}{\sqrt {2T}}}\right)\right]\right\}\,}$

where ${\displaystyle \operatorname {erf} }$ denotes the error function and ${\displaystyle \operatorname {sgn} }$ denotes the sign function. The above follows immediately from expressions for the Laplace transform of the distribution of the conditional first passage time of Brownian motion to a particular level.[34]

### Foreign exchange

Further information: Foreign exchange derivative

If we denote by S the FOR/DOM exchange rate (i.e., 1 unit of foreign currency is worth S units of domestic currency) we can observe that paying out 1 unit of the domestic currency if the spot at maturity is above or below the strike is exactly like a cash-or nothing call and put respectively. Similarly, paying out 1 unit of the foreign currency if the spot at maturity is above or below the strike is exactly like an asset-or nothing call and put respectively. Hence if we now take ${\displaystyle r_{FOR}}$, the foreign interest rate, ${\displaystyle r_{DOM}}$, the domestic interest rate, and the rest as above, we get the following results.

In case of a digital call (this is a call FOR/put DOM) paying out one unit of the domestic currency we get as present value,

${\displaystyle C=e^{-r_{DOM}T}\Phi (d_{2})\,}$

In case of a digital put (this is a put FOR/call DOM) paying out one unit of the domestic currency we get as present value,

${\displaystyle P=e^{-r_{DOM}T}\Phi (-d_{2})\,}$

While in case of a digital call (this is a call FOR/put DOM) paying out one unit of the foreign currency we get as present value,

${\displaystyle C=Se^{-r_{FOR}T}\Phi (d_{1})\,}$

and in case of a digital put (this is a put FOR/call DOM) paying out one unit of the foreign currency we get as present value,

${\displaystyle P=Se^{-r_{FOR}T}\Phi (-d_{1})\,}$

### Skew

In the standard Black–Scholes model, one can interpret the premium of the binary option in the risk-neutral world as the expected value = probability of being in-the-money * unit, discounted to the present value. The Black–Scholes model relies on symmetry of distribution and ignores the skewness of the distribution of the asset. Market makers adjust for such skewness by, instead of using a single standard deviation for the underlying asset ${\displaystyle \sigma }$ across all strikes, incorporating a variable one ${\displaystyle \sigma (K)}$ where volatility depends on strike price, thus incorporating the volatility skew into account. The skew matters because it affects the binary considerably more than the regular options.

A binary call option is, at long expirations, similar to a tight call spread using two vanilla options. One can model the value of a binary cash-or-nothing option, C, at strike K, as an infinitesimally tight spread, where ${\displaystyle C_{v}}$ is a vanilla European call:[1][2]

${\displaystyle C=\lim _{\epsilon \to 0}{\frac {C_{v}(K-\epsilon )-C_{v}(K)}{\epsilon }}}$

Thus, the value of a binary call is the negative of the derivative of the price of a vanilla call with respect to strike price:

${\displaystyle C=-{\frac {dC_{v}}{dK}}}$

When one takes volatility skew into account, ${\displaystyle \sigma }$ is a function of ${\displaystyle K}$:

${\displaystyle C=-{\frac {dC_{v}(K,\sigma (K))}{dK}}=-{\frac {\partial C_{v}}{\partial K}}-{\frac {\partial C_{v}}{\partial \sigma }}{\frac {\partial \sigma }{\partial K}}}$

The first term is equal to the premium of the binary option ignoring skew:

${\displaystyle -{\frac {\partial C_{v}}{\partial K}}=-{\frac {\partial (S\Phi (d_{1})-Ke^{-rT}\Phi (d_{2}))}{\partial K}}=e^{-rT}\Phi (d_{2})=C_{noskew}}$

${\displaystyle {\frac {\partial C_{v}}{\partial \sigma }}}$ is the Vega of the vanilla call; ${\displaystyle {\frac {\partial \sigma }{\partial K}}}$ is sometimes called the "skew slope" or just "skew". Skew is typically negative, so the value of a binary call is higher when taking skew into account.

${\displaystyle C=C_{noskew}-Vega_{v}*Skew}$

## Relationship to vanilla options' Greeks

Since a binary call is a mathematical derivative of a vanilla call with respect to strike, the price of a binary call has the same shape as the delta of a vanilla call, and the delta of a binary call has the same shape as the gamma of a vanilla call.

## References

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3. ^ a b Binary Option Definition Investopedia. Retrieved 2013-06-30.
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6. ^ "warning against unauthorised websites offering binary options trading". AMF. Retrieved 14 January 2012.
7. ^ "regarding the supervision of Binary Options" (PDF). CySEC. 3 May 2012. Retrieved 4 June 2012.
8. ^ Gaming or Trading? That is the Question – MFSA To Regulate Binary Options as a Financial Product
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16. ^ "Binary Options and Fraud". Retrieved 23 May 2014.
17. ^ WSJ: Banc de Binary Reaches $11 Million Settlement with U.S. Authorities 18. ^ A to Z Forex: Breaking: CySEC fines Banc De Binary €350,000 19. ^ Finance Magnates: Banc De Binary Fined €125,000 by Cyprus Watchdog for Soliciting American Clients 20. ^ Finance Magnates: Breaking: Banc De Binary Settles With CySEC to Pay €350,000 21. ^ "Federal Court Orders Israeli Web-based Firms, Vault Options, Ltd. and Global Trader 365, to Pay More than$4.5 Million for Unlawful Off-Exchange Binary Options Trading, Fraud, and Registration Violations". Commodities and Futures Trading Commission. July 28, 2016.
22. ^ Weinglass, Simona, and Horovitz, David (November 12, 2016). "Israeli authorities raid binary options firm, arrest CEO, salespeople". Times of Israel.
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26. ^ Securities and Exchange Commission, Release No. 34-56471; File No. SR-OCC-2007-08, September 19, 2007. “Self-Regulatory Organizations; The Options Clearing Corporation; Notice of Filing of a Proposed Rule Change Relating to Binary Options”.
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29. ^ a b BINARY OPTIONS ON SPXSM AND VIX®. cboe.com
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