Binary option
Encyclopedia
In finance
, a binary option is a type of option
where the payoff is either some fixed amount of some asset
or nothing at all. 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. Thus, the options are binary in nature because there are only two possible outcomes. 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
). Binary options are usually European-style
options.
For example, a purchase is made of a binary cash-or-nothing call option on XYZ Corp's stock struck at $100 with a binary payoff of $1000. Then, if at the future maturity date, the stock is trading at or above $100, $1000 is received. If its stock is trading below $100, nothing is received.
In the popular Black-Scholes model, the value of a digital option can be expressed in terms of the cumulative normal distribution function.
, 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.
Since mid-2008 binary options web-sites called binary option trading platforms
have been offering a simplified version of exchange-traded binary options. It is estimated that around 30 such platforms (including white label products) have been in operation as of January 2011, offering options on some 70 underlying assets.
proposed a rule change to allow binary options, and the Securities and Exchange Commission approved listing cash-or-nothing binary options in 2008. 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"; 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. The American Stock Exchange and Donato A. Montanaro
submitted a patent application for exchange-listed binary options using a volume-weighted settlement index in 2005.
CBOE offers binary options on the S&P 500
(SPX) and the CBOE Volatility Index (VIX)
. The tickers for these are BSZ and BVZ, respectively. 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.
In 2009 Nadex, the North American Derivatives Exchange, launched and now offers a suite of binary options vehicles.. Nadex binary options are available on a range Stock Index Futures, Spot Forex, Commodity Futures, and Economic Events.
In 2011, the American website Binaryoptionsnow.com released the first comprehensive infographic on binary options available here
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 strike price will close at or below 1.2500 at 3:00 p.m. can buy a put option
or sell the contract.
At 2:00 p.m. the EUR/USD spot 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 make a gross profit of $100 x 10 = $1000. If the EUR/USD strike price will close at or above 1.2500 at 3:00 p.m. the trader's net profit will be the payoff at expiry minus the cost of the option: $1000 - $400 = $600.
The trader can also choose to liquidate (buy or sell 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 $1000. The trader's net profit is $600.
, T is the time to maturity, q is the dividend rate, r is the risk-free interest rate
and
is the volatility
.
denotes the cumulative distribution function
of the normal distribution,
and,
Hence if we now take
, the foreign interest rate, 
, 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,
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,
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,
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,
To take volatility skew into account, a more sophisticated analysis based on call spreads can be used.
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 infinitessimally tight spread, where
is a vanilla European call:,
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:
When one takes volatility skew into account,
is a function of 
:
The first term is equal to the premium of the binary option ignoring skew:
is the Vega
of the vanilla call;
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.
, binary options are used to find out a population's best estimate of an event occurring - for example, a price of 0.65 on a binary option triggered by the Democratic candidate winning the next US Presidential election can be interpreted as an estimate of 65% likelihood of him winning.
In financial markets, expected return
s on a stock or other instrument are already priced into the stock. However, a binary options market provides other information. Just as the regular options market reveals the market's estimate of variance (volatility), i.e. the second moment
, a binary options market reveals the market's estimate of skew, i.e. the third moment.
In theory, a portfolio of binary options can also be used to synthetically recreate (or valuate) any other option
(analogous to integration), although in practical terms this is not possible due to the lack of depth of the market for these relatively thinly traded securities.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, a binary option is a type of option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
where the payoff is either some fixed amount of some asset
Asset
In financial accounting, assets are economic resources. Anything tangible or intangible that is capable of being owned or controlled to produce value and that is held to have positive economic value is considered an asset...
or nothing at all. 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. Thus, the options are binary in nature because there are only two possible outcomes. 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
American Stock Exchange
NYSE Amex Equities, formerly known as the American Stock Exchange is an American stock exchange situated in New York. AMEX was a mutual organization, owned by its members. Until 1953, it was known as the New York Curb Exchange. On January 17, 2008, NYSE Euronext announced it would acquire the...
). Binary options are usually European-style
Option style
In finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American options. These options - as well as others where the...
options.
For example, a purchase is made of a binary cash-or-nothing call option on XYZ Corp's stock struck at $100 with a binary payoff of $1000. Then, if at the future maturity date, the stock is trading at or above $100, $1000 is received. If its stock is trading below $100, nothing is received.
In the popular Black-Scholes model, the value of a digital option can be expressed in terms of the cumulative normal distribution function.
Non exchange-traded binary options
Binary option contracts have long been available Over-the-counter (OTC)Over-the-counter (finance)
Within the derivatives markets, many products are traded through exchanges. An exchange has the benefit of facilitating liquidity and also mitigates all credit risk concerning the default of a member of the exchange. Products traded on the exchange must be well standardised to transparent trading....
, i.e. sold directly by the issuer to the buyer. They were generally considered "exotic
Exotic option
In finance, an exotic option is a derivative which has features making it more complex than commonly traded products . These products are usually traded over-the-counter , or are embedded in structured notes....
" 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.
Since mid-2008 binary options web-sites called binary option trading platforms
Binary options trading platform
Binary options trading platform is a web-based, over-the-counter, real-time trading arena, which offers nonprofessional investors a way to profit from correct, short term predictions of some underlying asset price movement by buying binary options on that asset.Binary options platforms have been...
have been offering a simplified version of exchange-traded binary options. It is estimated that around 30 such platforms (including white label products) have been in operation as of January 2011, offering options on some 70 underlying assets.
Exchange-traded binary options
In 2007, the Options Clearing CorporationOptions Clearing Corporation
Options Clearing Corporation or OCC, founded in 1973, is the world's largest equity derivatives clearing organization, providing central counterparty clearing and settlement services to 14 exchanges and platforms for options, financial and commodity futures, security futures and securities...
proposed a rule change to allow binary options, and the Securities and Exchange Commission approved listing cash-or-nothing binary options in 2008. In May 2008, the American Stock Exchange
American Stock Exchange
NYSE Amex Equities, formerly known as the American Stock Exchange is an American stock exchange situated in New York. AMEX was a mutual organization, owned by its members. Until 1953, it was known as the New York Curb Exchange. On January 17, 2008, NYSE Euronext announced it would acquire the...
(Amex) launched exchange-traded European cash-or-nothing binary options, and the Chicago Board Options Exchange
Chicago Board Options Exchange
The Chicago Board Options Exchange , located at 400 South LaSalle Street in Chicago, is the largest U.S. options exchange with annual trading volume that hovered around one billion contracts at the end of 2007...
(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"; 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. The American Stock Exchange and Donato A. Montanaro
Donato A. Montanaro
Donato Montanaro is Chairman & CEO of online brokerage firm TradeKing, which he co-founded in December 2005. He also helped found online brokerage SureTrade, a subsidiary of Quick & Reilly that was acquired by Fleet Financial Group, now FleetBoston Financial....
submitted a patent application for exchange-listed binary options using a volume-weighted settlement index in 2005.
CBOE offers binary options on the S&P 500
S&P 500
The S&P 500 is a free-float capitalization-weighted index published since 1957 of the prices of 500 large-cap common stocks actively traded in the United States. The stocks included in the S&P 500 are those of large publicly held companies that trade on either of the two largest American stock...
(SPX) and the CBOE Volatility Index (VIX)
VIX
VIX is the ticker symbol for the Chicago Board Options Exchange Market Volatility Index, a popular measure of the implied volatility of S&P 500 index options. Often referred to as the fear index or the fear gauge, it represents one measure of the market's expectation of stock market volatility over...
. The tickers for these are BSZ and BVZ, respectively. 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.
In 2009 Nadex, the North American Derivatives Exchange, launched and now offers a suite of binary options vehicles.. Nadex binary options are available on a range Stock Index Futures, Spot Forex, Commodity Futures, and Economic Events.
In 2011, the American website Binaryoptionsnow.com released the first comprehensive infographic on binary options available here
Example of a Binary Options Trade
A trader who thinks that the EUR/USD strike priceStrike price
In options, the strike price is a key variable in a derivatives contract between two parties. Where the contract requires delivery of the underlying instrument, the trade will be at the strike price, regardless of the spot price of the underlying instrument at that time.Formally, the strike...
will close at or above 1.2500 at 3:00 p.m. can buy a call option
Call option
A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...
on that outcome. A trader who thinks that the EUR/USD strike price will close at or below 1.2500 at 3:00 p.m. can buy a put option
Put option
A put or put option is a contract between two parties to exchange an asset, the underlying, at a specified price, the strike, by a predetermined date, the expiry or maturity...
or sell the contract.
At 2:00 p.m. the EUR/USD spot price
Spot price
The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate settlement . Spot settlement is normally one or two business days from trade date...
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 make a gross profit of $100 x 10 = $1000. If the EUR/USD strike price will close at or above 1.2500 at 3:00 p.m. the trader's net profit will be the payoff at expiry minus the cost of the option: $1000 - $400 = $600.
The trader can also choose to liquidate (buy or sell 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 the Money
In the Money is a comedy film starring The Bowery Boys. The film was released on February 16, 1958 by Allied Artists Pictures and is the forty-eighth and final film in the series. It was directed by William Beaudine and written by Al Martin and Elwood Ullman.-Plot summary:Sach is hired to take...
.
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 $1000. 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. In these, S is the initial stock price, K denotes the strike priceStrike price
In options, the strike price is a key variable in a derivatives contract between two parties. Where the contract requires delivery of the underlying instrument, the trade will be at the strike price, regardless of the spot price of the underlying instrument at that time.Formally, the strike...
, T is the time to maturity, q is the dividend rate, r is the risk-free interest rate
Risk-free interest rate
Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time....
and
is the volatilityVolatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
.
denotes the cumulative distribution functionCumulative distribution function
In probability theory and statistics, the cumulative distribution function , or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x. Intuitively, it is the "area so far"...
of the normal distribution,
and,
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,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,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,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,Foreign exchange
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
, the foreign interest rate, , 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,
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,
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,
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,
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.To take volatility skew into account, a more sophisticated analysis based on call spreads can be used.
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 infinitessimally tight spread, where
is a vanilla European call:,Thus, the value of a binary call is the negative of the derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
of the price of a vanilla call with respect to strike price:
When one takes volatility skew into account,
is a function of :The first term is equal to the premium of the binary option ignoring skew:
is the VegaGreeks (finance)
In mathematical finance, the Greeks are the quantities representing the sensitivities of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of...
of the vanilla call;
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.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.Interpretation of prices
In a prediction marketPrediction market
Prediction markets are speculative markets created for the purpose of making predictions...
, binary options are used to find out a population's best estimate of an event occurring - for example, a price of 0.65 on a binary option triggered by the Democratic candidate winning the next US Presidential election can be interpreted as an estimate of 65% likelihood of him winning.
In financial markets, expected return
Expected return
The expected return is the weighted-average outcome in gambling, probability theory, economics or finance.It isthe average of a probability distribution of possible returns, calculated by using the following formula:...
s on a stock or other instrument are already priced into the stock. However, a binary options market provides other information. Just as the regular options market reveals the market's estimate of variance (volatility), i.e. the second moment
Moment (mathematics)
In mathematics, a moment is, loosely speaking, a quantitative measure of the shape of a set of points. The "second moment", for example, is widely used and measures the "width" of a set of points in one dimension or in higher dimensions measures the shape of a cloud of points as it could be fit by...
, a binary options market reveals the market's estimate of skew, i.e. the third moment.
In theory, a portfolio of binary options can also be used to synthetically recreate (or valuate) any other option
(analogous to integration), although in practical terms this is not possible due to the lack of depth of the market for these relatively thinly traded securities.