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{{Short description|Financial exotic option with an all-or-nothing payoff}}
{{Prone to spam|date=January 2014}}
A '''binary option''' is a [[
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]].<ref name="Globes 12-15-16" /> Many binary option outlets have been exposed as fraudulent.<ref>{{Cite web |url=https://www.fbi.gov/news/stories/binary-options-fraud |title=Binary Options Fraud |website=Federal Bureau of Investigation |language=en-us |access-date=2017-05-30}}</ref> The U.S. [[Federal Bureau of Investigation|FBI]] is investigating binary option scams throughout the world, and the Israeli police have tied the industry to criminal syndicates.<ref name="FBI">{{cite news |last1=Weinglass |first1=Simona |authorlink=Simona Weinglass|title=FBI says it's investigating binary options fraud worldwide, invites victims to come forward |url=http://www.timesofisrael.com/fbi-says-its-investigating-binary-options-fraud-worldwide-invites-victims-to-come-forward/ |access-date=February 15, 2017 |work =[[The Times of Israel]] |date=February 15, 2017}}</ref><ref name="ToIidesofM"/><ref name=":1" /> The [[European Securities and Markets Authority]] (ESMA) has banned retail binary options trading.<ref name="esma.europa.eu">{{Cite web |url=https://www.esma.europa.eu/press-news/esma-news/esma-agrees-prohibit-binary-options-and-restrict-cfds-protect-retail-investors |title=ESMA agrees to prohibit binary options and restrict CFDs to protect retail investors |website=www.esma.europa.eu|access-date=2019-03-21}}</ref> [[Australian Securities & Investments Commission]] (ASIC) considers binary options as a "high-risk" and "unpredictable" investment option, <ref>{{Cite news |url=http://www.ibtimes.com.au/binary-options-trading-australia-how-safe-it-1568192 |title=Binary Options Trading In Australia: How Safe Is It? |date=2018-05-14 |work=International Business Times AU |access-date=2018-05-22 |language=en}}</ref> and finally also banned binary options sale to retail investors in 2021.<ref name="asic.gov.au">{{cite web |url=https://asic.gov.au/about-asic/news-centre/find-a-media-release/2021-releases/21-064mr-asic-bans-the-sale-of-binary-options-to-retail-clients|title=21-064MR ASIC bans the sale of binary options to retail clients |website=[[Australian Securities & Investments Commission]]|access-date=8 March 2022}}</ref>
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Binary options "are based on a simple 'yes' or 'no' proposition: Will an underlying asset be above a certain price at a certain time?"<ref name="investopedia-guide">{{cite web |last1=Mitchell |first1=Cory |title=A Guide To Trading Binary Options In The U.S. |url=https://www.investopedia.com/articles/active-trading/061114/guide-trading-binary-options-us.asp |website=Investopedia |access-date=4 May 2018 |date=11 June 2014}}</ref> 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.<ref name="investopedia-guide"/>
[[Investopedia]] described the binary options trading process in the U.S. thus:
<blockquote>[A] 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).<ref name="investopedia-guide"/></blockquote>
In the U.S., every binary option settles at $100 or $0, $100 if the bet is correct, 0 if it is not.<ref name="investopedia-guide"/>
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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."<ref name="CFTC investor warning">{{cite web |url=https://www.cftc.gov/ConsumerProtection/FraudAwarenessPrevention/CFTCFraudAdvisories/fraudadv_binaryoptions.html |title=CFTC Fraud Advisories |website=www.cftc.gov |publisher=U.S. Commodity Futures Trading Commission |access-date= 4 May 2018}}</ref>
==Black–Scholes valuation==
In the [[Black–Scholes model]], the price of the option can be found by the formulas below.<ref>{{Cite book |last=Hull |first=John C. |year=2005 |title=Options, Futures and Other Derivatives |publisher=[[Prentice Hall]] |isbn=0-13-149908-4}}</ref> In fact, the [[Black–Scholes formula]] for the price of a vanilla [[call option]] (or [[put option]]) can be [[Black–Scholes#Interpretation|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 <math> \sigma </math> is the [[volatility (finance)|volatility]]. <math>\Phi</math> denotes the [[cumulative distribution function]] of the [[normal distribution]],
:<math> \Phi(x) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^x e^{-z^2/2} dz. </math>
and,
:<math> d_1 = \frac{\ln\frac{S}{K} + (r-q+\sigma^{2}/2)T}{\sigma\sqrt{T}}. </math>
: <math> d_2 = d_1-\sigma\sqrt{T}. </math>
===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
:<math> C = e^{-rT}\Phi(d_2). \,</math>
===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
:<math> P = e^{-rT}\Phi(-d_2). \,</math>
===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
:<math> C = Se^{-qT}\Phi(d_1). \,</math>
===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:
:<math> P = Se^{-qT}\Phi(-d_1). \,</math>
===American style===
[[File:American binary put.png|thumb|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 <math>T</math>. That is, denoting by <math>K</math> the strike price, if <math>K\geq S</math> (resp. <math>K\leq S</math>), the corresponding American binary put (resp. call) is worth exactly one unit. Let
:<math> a=\frac{1}{\sigma}\ln(K/S)\text{, }\xi=\frac{r-q}{\sigma}-\frac{\sigma}{2}\text{, and }b=\sqrt{\xi^{2}+2r}. \,</math>
The price of a cash-or-nothing American binary put (resp. call) with strike <math>K<S</math> (resp. <math>K>S</math>) and time-to-expiry <math>T</math> is:
:<math> \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\} \,</math>
where <math>\operatorname{erf}</math> denotes the [[error function]] and <math>\operatorname{sgn}</math> 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.<ref>[http://parsiad.ca/post/closed-form-expressions-for-perpetual-and-finite-maturity-american-binary-options Closed-form expressions for perpetual and finite-maturity American binary options]{{Dead link|date=June 2019 |bot=InternetArchiveBot |fix-attempted=yes }}. parsiad.ca (2015-03-01). Retrieved on 2016-07-18.</ref>
===Foreign exchange===
{{Further|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 <math>r_{\mathrm{FOR}}</math>, the foreign interest rate, <math>r_{DOM}</math>, 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,
:<math> C = e^{-r_{\mathrm{DOM}} T}\Phi(d_2) \,</math>
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,
:<math> P = e^{-r_{\mathrm{DOM}}T}\Phi(-d_2) \,</math>
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,
:<math> C = Se^{-r_{\mathrm{FOR}} T}\Phi(d_1) \,</math>
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,
:<math> P = Se^{-r_{\mathrm{FOR}}T}\Phi(-d_1) \,</math>
===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 <math>\sigma</math> across all strikes, incorporating a variable one <math>\sigma(K)</math> 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 <math>C_v</math> is a vanilla European call:<ref name="Breeden, D. T. 1978"/><ref name="Gatheral, J. 2006"/>
:<math> C = \lim_{\epsilon \to 0} \frac{C_v(K-\epsilon) - C_v(K)}{\epsilon} </math>
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:
:<math> C = -\frac{dC_v}{dK} </math>
When one takes volatility skew into account, <math>\sigma</math> is a function of <math>K</math>:
:<math> 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}</math>
The first term is equal to the premium of the binary option ignoring skew:
:<math> -\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_{\mathrm{noskew}}</math>
<math>\frac{\partial C_v}{\partial \sigma}</math> is the [[Greeks (finance)|Vega]] of the vanilla call; <math>\frac{\partial \sigma}{\partial K}</math> 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.
:<math> C = C_{\mathrm{noskew}} - \mathrm{Vega}_v * \mathrm{Skew}</math>
===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.
==Regulation and fraud==
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=== France ===
In August 2016, France's [[Law on transparency, the fight against corruption and the modernization of economic life|''Sapin II'' bill on transparency]] was announced by the [[Autorité des marchés financiers (France)|Autorité des Marchés Financiers]] (AMF), seeking to outlaw all financial derivatives advertising. The AMF stated that it would ban the advertising of certain highly speculative and risky financial contracts to private individuals by electronic means.<ref>{{citation|type=press release|title=Ban on the advertising of forex products, binary options and some CFDs: AMF launches consultation on changes to its General Regulation|date=August 1, 2016|work=Autorité des Marchés Financiers|url=http://www.amf-france.org/en_US/Actualites/Communiques-de-presse/AMF/annee-2016.html?docId=workspace%3A%2F%2FSpacesStore%2Fad42eecc-9720-49da-82a8-2ddcb72fbf1d|access-date=January 15, 2017|archive-url=https://web.archive.org/web/20190617015956/https://www.amf-france.org/en_US/Actualites/Communiques-de-presse/AMF/annee-2016.html?docId=workspace%3A%2F%2FSpacesStore%2Fad42eecc-9720-49da-82a8-2ddcb72fbf1d|archive-date=June 17, 2019|url-status=dead}}</ref><ref>{{cite news |url=http://financefeeds.com/ig-group-officially-responds-french-fx-cfd-advertising-ban/ |title=IG Group officially responds to French FX and CFD advertising ban |work=Finance Feeds |date=9 January 2017 |author=Andrew Saks-McLeod |access-date=18 May 2017 |archive-date=3 September 2017 |archive-url=https://web.archive.org/web/20170903034136/https://financefeeds.com/ig-group-officially-responds-french-fx-cfd-advertising-ban/ |url-status=dead }}</ref> The document applies specifically to binary options, and to [[contracts for difference]] (CFDs), and financial contracts on currencies. The French regulator is determined to cooperate with the legal authorities to have illegal websites blocked.<ref>{{cite news|url=http://financefeeds.com/breaking-amf-toughens-stance-advertising-following-public-consultation/|title=AMF toughens its stance on advertising following public consultation|work=Finance Feeds|date=10 January 2017|author=Maria Nikolova|access-date=18 May 2017|archive-date=7 May 2017|archive-url=https://web.archive.org/web/20170507140401/http://financefeeds.com/breaking-amf-toughens-stance-advertising-following-public-consultation/|url-status=dead}}</ref> The law also prohibits all forms of sponsorship and partnership that results in direct or indirect advertising of the financial products it covers. This ban was seen by industry watchers as having an impact on sponsored sports such as European football clubs.<ref>{{citation|title=French football clubs rush to terminate binary options partnerships|quote=Under Article 77 of the Sapin II law, football teams have until the end of June this year to terminate all sponsorships|author=Maria Nikolova|work=Finance Feeds|url=http://financefeeds.com/french-football-clubs-rush-terminate-binary-options-partnerships/|access-date=2017-01-15|archive-date=2019-06-17|archive-url=https://web.archive.org/web/20190617015948/https://financefeeds.com/french-football-clubs-rush-terminate-binary-options-partnerships/|url-status=dead}}</ref>
The Cyprus-based company 24Option<ref>{{Cite web|url=https://cyprusregistry.com/companies/EE/41700|title=24OPTION - Cyprus Business Name - CyprusRegistry.com|website=cyprusregistry.com|access-date=2019-04-17}}</ref> was banned from trading in France by AMF earlier in 2016.<ref>{{citation|type=press release|title=L'Autorité des marchés financiers interdit à Rodeler Limited (" 24option ") de fournir des services sur le territoire français|trans-title=Autorité des Marchés Financiers halts Rodeler Limited ("24option") activities in France|date=July 29, 2016|publisher=Autorité des Marchés Financiers|url=http://www.amf-france.org/Actualites/Communiques-de-presse/AMF/annee-2016.html?docId=workspace%3A%2F%2FSpacesStore%2Ff35a247e-e20d-42c3-8b3d-b354794a2a70|access-date=January 15, 2017|archive-url=https://web.archive.org/web/20190617015955/https://www.amf-france.org/Actualites/Communiques-de-presse/AMF/annee-2016.html?docId=workspace%3A%2F%2FSpacesStore%2Ff35a247e-e20d-42c3-8b3d-b354794a2a70|archive-date=June 17, 2019|url-status=dead}}</ref> They had sponsored a well-known Irish [[mixed martial arts|mixed martial artist]], [[Conor McGregor]], who in turn promoted the company through social media.<ref>{{citation|title=Conor McGregor sponsor barred from operating in France|work=Irish Times|date=November 19, 2016|author=Barry O'Halloran|url=http://www.irishtimes.com/business/media-and-marketing/conor-mcgregor-sponsor-barred-from-operating-in-france-1.2874175}}</ref>
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=== Indonesia ===
According to the Commodity Futures Trading Regulatory Agency (CoFTRA) in Indonesia, also known as BAPPEBTI, binary options are considered a form of online gambling and is illegal in the country. The move to delegalize binary options stems from concerns that the public may be swayed by misleading advertisements, promotions, and offers to participate in fraudulent practices that operate under the guise of binary options trading.<ref>{{Cite web|last=Dirgantara|first=Hikma|date=2022-02-03|title=Bappebti Blokir 92 Entitas Binary Option di 2021, Termasuk Binomo, IQ Option|url=https://investasi.kontan.co.id/news/bappebti-blokir-92-entitas-binary-option-di-2021-termasuk-binomo-iq-option|access-date=2022-02-07|website=Kontan.co.id|language=id}}</ref> As of 2 February 2022, at least 92 binary options websites, including Binomo, [[IQ Option]], and Olymp Trade, have been classified as unlicensed operators and blocked by the Indonesian government.<ref>{{Cite web|date=2022-02-04|title=Indonesian regulators block illegal trading websites following complaints on social media|url=https://kr-asia.com/indonesian-regulators-block-illegal-trading-websites-following-complaints-on-social-media|access-date=2022-02-07|website=KrASIA|language=en}}</ref>
=== Israel ===
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;Fraud
In 2016 ''[[The Times of Israel]]'' ran several articles on binary options fraud. "The wolves of Tel Aviv: Israel's vast, amoral binary options scam exposed" revealed that the industry is a scam.<ref name="israeltimes1" /> A second article describes in detail how a 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
In July 2016 the Israeli binary option firms Vault Options and Global Trader 365 were ordered by the [[United States District Court for the Northern District of Illinois|U.S. District Court for the Northern District of 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 United States or selling to U.S. residents.<ref>{{cite news|url=http://www.cftc.gov/PressRoom/PressReleases/pr7414-16|title= 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|date=July 28, 2016|publisher=Commodities and Futures Trading Commission}}</ref>
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In September 2017, the FBI arrested Lee Elbaz, CEO of binary options trading company Yukom Communications, upon her arrival in the United States. They arrested her for [[wire fraud]] and conspiracy to commit wire fraud.<ref name="Matts092417">{{cite news |last1=Staff|first1=Tori|title=FBI arrests Israeli binary options CEO as she disembarks El Al flight at JFK|url=https://www.timesofisrael.com/fbi-arrests-israeli-binary-options-ceo-as-she-disembarks-el-al-flight-at-jfk/|work =The Times of Israel|date=September 24, 2017|access-date=September 24, 2017}}</ref> In 2019, Lee Elbaz was found guilty and sentenced to 22 years in prison.<ref>{{cite news |title=Former CEO of Israeli Company Sentenced to 22 Years in Prison for Orchestrating Major International Binary Options Fraud Scheme|url=https://www.justice.gov/opa/pr/former-ceo-israeli-company-sentenced-22-years-prison-orchestrating-major-international-binary/|work =Department of Justice|date=December 19, 2019|access-date=August 19, 2022}}</ref>
In February 2019, the FBI arrested Austin Smith, founder of Wealth Recovery International, after his arrival in the United States. Smith was arrested for
===Malta===
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In the United States, the [[Securities and Exchange Commission]] (SEC) approved [[Exchange-traded product|exchange-traded]] binary options in 2008.<ref>{{Cite news|url=https://www.reuters.com/article/companyNewsAndPR/idUSN0943920080609|title=CBOE to list binary options on S&P 500, VIX |last=Frankel |first = Doris |date=June 9, 2008 | publisher=[[Reuters]] | access-date=December 8, 2018}}</ref> Trading commenced on the [[NYSE American]] (MYSEA) and the [[Chicago Board Options Exchange]] (CBOE) in May and June 2008.<ref name=leapinfo>{{cite web | url=https://www.leaprate.com/news/the-history-of-binary-options-trading-infographic/ | title=The History of Binary Options Trading – Infographic | date=January 5, 2017 | website=leaprate.com | access-date=December 8, 2018}}</ref>
The MYSEA offers binary options on some [[exchange-traded fund]]s and a few highly liquid equities such as [[Citigroup]] and [[Google]]. On the exchange binary options were called "fixed return options" (FROs). To reduce the threat of [[market manipulation]] of single stocks, FROs use a "settlement index" defined as a volume-weighted average of trades on the expiration day. MYSEA and [[Donato A. Montanaro]] submitted a [[patent application]] for exchange-listed binary options using a volume-weighted settlement index in 2005.<ref>[
[[Nadex|NADEX]], a U.S.-based [[Commodity Futures Trading Commission]] (CFTC) regulated exchange, launched binary options for a range of [[Forex]], [[Commodity#Commodity trade|commodities]], and [[stock indices]]' markets in June 2009,.<ref>{{cite web|url=http://www.nadex.com/content/files/pressrelease-01.pdf|title=Nadex, North American derivatives exchange rolls out new trading platform, products|date=June 22, 2009|publisher=[[Nadex]]|archive-url=https://web.archive.org/web/20120401080606/http://www.nadex.com/content/files/pressrelease-01.pdf|archive-date=April 1, 2012|access-date=December 8, 2018}}</ref> On March 30, 2010 the CFTC issued an amended Order of Designation to allow trades on NADEX to be intermediated.<ref>{{Cite web|url=https://sirt.cftc.gov/SIRT/SIRT.aspx?Topic=TradingOrganizationsAD&Key=34536|title=- CFTC|website=sirt.cftc.gov|access-date=2019-03-21}}</ref> NADEX have since offered binary options trading between buyers and sellers. They do not participate in the trades.<ref>{{Cite web|url=https://www.nadex.com/why-nadex/regulated-and-legal-for-us-residents|title=Regulated & Legal for US Residents|date=2015-09-24|website=Nadex|language=en|access-date=2019-03-21}}</ref>
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== External links ==
*[
*[https://www.cftc.gov/ConsumerProtection/FraudAwarenessPrevention/CFTCFraudAdvisories/fraudadv_binaryoptions.html CFTC investor alert]
*{{cite news|last1=Levy-Weinrib|first1=Ela|title=Regulator seeks blanket binary options ban|url=http://www.globes.co.il/en/article-regulator-seeks-blanket-binary-options-prohibition-1001175186|access-date=May 6, 2018|publisher=[[Globes (newspaper)|Globes]] English|date=February 2, 2017}}
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