In finance, the style or family of an 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...

 is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised

Exercise (options)

The owner of an option contract may exercise it, indicating that the financial transaction specified by the contract is to be enacted immediately between the two parties, and the contract itself is terminated...

. The vast majority of options are either European or American (style) options. These options - as well as others where the payoff is calculated similarly - are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic option

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....

s". Exotic options can pose challenging problems in valuation and hedging

Hedge (finance)

A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...

.

American and European options

The key difference between American and European options relates to when the options can be exercised:

• A European option may be exercised only at the expiry date of the option, i.e. at a single pre-defined point in time.
• An American option on the other hand may be exercised at any time before the expiry date.

For both, the pay-off - when it occurs - is via:

Max [ (S – K), 0 ], for 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...

Max [ (K – S), 0 ], for 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...

:

(Where K is the Strike price

Strike 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...

 and S is the spot price of the underlying asset)

Option contract

Option contract

An option contract is defined as "a promise which meets the requirements for the formation of a contract and limits the promisor's power to revoke an offer." Restatement of Contracts § 25 ....

s traded on futures exchange

Futures exchange

A futures exchange or futures market is a central financial exchange where people can trade standardized futures contracts; that is, a contract to buy specific quantities of a commodity or financial instrument at a specified price with delivery set at a specified time in the future. These types of...

s are mainly American-style, whereas those traded over-the-counter

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....

 are mainly European.

Nearly all stock and equity options are American options, while indexes are generally represented by European options. A list of European and American options can be found on the Options Industry Council website.

Expiration date

Traditional monthly American options expire the third Saturday of every month. They are closed for trading the Friday prior.

European options expire the Friday prior to the third Saturday of every month. Therefore they are closed for trading the Thursday prior to the third Saturday of every month.

Difference in value

European options are typically valued using the Black–Scholes or Black model

Black model

The Black model is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing bond options, interest rate caps / floors, and swaptions...

 formula. This is a simple equation with a closed-form solution that has become standard in the financial community. There are no general formulae for American options, but a choice of models to approximate the price are available (for example Whaley, binomial options model, and others - there is no consensus on which is preferable).

An investor holding an American-style option and seeking optimal value will only exercise it before maturity under certain circumstances. Any option has a non-negative time value

Option time value

In finance, the time value of an option is the premium a rational investor would pay over its current exercise value , based on its potential to increase in value before expiring. This probability is always greater than zero, thus an option is always worth more than its current exercise value...

 and is usually worth more unexercised. Owners who wish to realise the full value of their option will mostly prefer to sell it on, rather than exercise it immediately, sacrificing the time value.

Where an American and a European option are otherwise identical (having the same strike price

Strike 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...

, etc.), the American option will be worth at least as much as the European (which it entails). If it is worth more, then the difference is a guide to the likelihood of early exercise. In practice, one can calculate the Black–Scholes price of a European option that is equivalent to the American option (except for the exercise dates of course). The difference between the two prices can then be used to calibrate the more complex American option model.

To account for the American's higher value there must be some situations in which it is optimal to exercise the American option before the expiration date. This can arise in several ways, such as:

• An 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...
  
   (ITM) 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 a stock
  Stock
  The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
  
   is often exercised just before the stock pays a dividend
  Dividend
  Dividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. When a corporation earns a profit or surplus, that money can be put to two uses: it can either be re-invested in the business , or it can be distributed to...
  
   which would lower its value by more than the option's remaining time value

• A deep ITM currency
  Currency
  In economics, currency refers to a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation's money supply...
  
   option (FX option) where the strike currency has a lower interest rate than the currency to be received will often be exercised early because the time value sacrificed is less valuable than the expected depreciation of the received currency against the strike.

• An American bond option
  Bond option
  In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC....
  
   on the dirty price
  Dirty price
  The dirty price of a bond represents the value of a bond, exclusive of any commissions or fees. The dirty price is also called the "full price" or the "all in price."-Bond Pricing:...
  
   of a bond
  Bond (finance)
  In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
  
   (such as some convertible bond
  Convertible bond
  In finance, a convertible note is a type of bond that the holder can convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price. It is a hybrid security with debt- and equity-like features...
  
  s) may be exercised immediately if ITM and a coupon
  Coupon (bond)
  A coupon payment on a bond is a periodic interest payment that the bondholder receives during the time between when the bond is issued and when it matures. Coupons are normally described in terms of the coupon rate, which is calculated by adding the total amount of coupons paid per year and...
  
   is due.

• 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...
  
   on gold
  Gold
  Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...
  
   will be exercised early when deep ITM, because gold tends to hold its value whereas the currency
  Currency
  In economics, currency refers to a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation's money supply...
  
   used as the strike is often expected to lose value through inflation
  Inflation
  In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...
  
   if the holder waits until final maturity to exercise the option (they will almost certainly exercise a contract deep ITM, minimizing its time value).

Non-vanilla exercise rights

There are other, more unusual exercise styles in which the pay-off value remains the same as a standard option (as in the classic American and European options above) but where early exercise occurs differently:

• A Bermudan option is an option where the buyer has the right to exercise at a set (always discretely spaced) number of times. This is intermediate between a European option—which allows exercise at a single time, namely expiry—and an American option, which allows exercise at any time (the name is a pun: Bermuda
  Bermuda
  Bermuda is a British overseas territory in the North Atlantic Ocean. Located off the east coast of the United States, its nearest landmass is Cape Hatteras, North Carolina, about to the west-northwest. It is about south of Halifax, Nova Scotia, Canada, and northeast of Miami, Florida...
  
  , a British overseas territory, is somewhat American and somewhat European - in terms of both option style and physical location - but is nearer to American in terms of both). For example a typical Bermudan swaption
  Swaption
  A swaption is an option granting its owner the right but not the obligation to enter into an underlying swap. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swaps....
  
   might confer the opportunity to enter into an interest rate swap
  Interest rate swap
  An interest rate swap is a popular and highly liquid financial derivative instrument in which two parties agree to exchange interest rate cash flows, based on a specified notional amount from a fixed rate to a floating rate or from one floating rate to another...
  
  . The option holder might decide to enter into the swap at the first exercise date (and so enter into, say, a ten-year swap) or defer and have the opportunity to enter in six months time (and so enter a nine-year and six-month swap); see Swaption: Valuation. Most exotic interest rate options are of Bermudan style.

• A Canary option is an option whose exercise style lies somewhere between European options and Bermudan options. (The name refers to the relative geography of the Canary Islands
  Canary Islands
  The Canary Islands , also known as the Canaries , is a Spanish archipelago located just off the northwest coast of mainland Africa, 100 km west of the border between Morocco and the Western Sahara. The Canaries are a Spanish autonomous community and an outermost region of the European Union...
  
  .) Typically, the holder can exercise the option at quarterly dates, but not before a set time period (typically one year) has elapsed. The term was coined by Keith Kline, who at the time was an agency fixed income trader at the Bank of New York.

• A capped-style option is not an interest rate cap but a conventional option with a pre-defined profit cap written into the contract. A capped-style option is automatically exercised when the underlying security closes at a price making the option's mark to market
  Mark to market
  Mark-to-market or fair value accounting refers to accounting for the fair value of an asset or liability based on the current market price of the asset or liability, or for similar assets and liabilities, or based on another objectively assessed "fair" value...
  
   match the specified amount.

• A compound option is an option on another option, and as such presents the holder with two separate exercise dates and decisions. If the first exercise date arrives and the 'inner' option's market price is below the agreed strike the first option will be exercised (European style), giving the holder a further option at final maturity.

• A shout option allows the holder effectively two exercise dates: during the life of the option they can (at any time) "shout" to the seller that they are locking-in the current price, and if this gives them a better deal than the pay-off at maturity they'll use the underlying price on the shout date rather than the price at maturity to calculate their final pay-off.

• A swing option gives the purchaser the right to exercise one and only one call or put on any one of a number of specified exercise dates (this latter aspect is Bermudan). Penalties are imposed on the buyer if the net volume purchased exceeds or falls below specified upper and lower limits. Allows the buyer to "swing" the price of the underlying asset. Primarily used in energy trading.

"Exotic" options with standard exercise styles

These options can be exercised either European style or American style; they differ from the plain vanilla option only in the calculation of their pay-off value:

• A cross option (or composite option) is an option on some underlying asset in one currency
  Currency
  In economics, currency refers to a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation's money supply...
  
   with a strike denominated in another currency. For example a standard 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 IBM, which is denominated in dollars pays $MAX(S-K,0) (where S is the stock price at maturity and K is the strike). A composite stock option might pay JPYMAX(S/Q-K,0), where Q is the prevailing FX rate. The pricing of such options naturally needs to take into account FX volatility and the correlation
  Correlation
  In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
  
   between the exchange rate
  Exchange rate
  In finance, an exchange rate between two currencies is the rate at which one currency will be exchanged for another. It is also regarded as the value of one country’s currency in terms of another currency...
  
   of the two currencies involved and the underlying stock price.

• A quanto
  Quanto
  A quanto is a type of derivative in which the underlying is denominated in one currency,but the instrument itself is settled in another currency at some fixed rate...
  
   option is a cross option in which the exchange rate is fixed at the outset of the trade, typically at 1. The payoff of an IBM quanto call option would then be JPYmax(S-K,0).

• An exchange option is the right to exchange one asset for another (such as a sugar future for a corporate bond
  Bond (finance)
  In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
  
  ).

• A basket option
  Basket option
  A basket option is a financial derivative, more specifically an exotic option, whose underlying is a sum or average of different assets. Examples are index options, options on a portfolio, etc....
  
  is an option on the weighted average of several underlyings

• A rainbow option
  Rainbow option
  Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. Rainbow options are usually calls or puts on the best or worst of n underlying assets, or options which...
  
  is a basket option where the weightings depend on the final performances of the components. A common special case is an option on the worst-performing of several stocks.

• A Low Exercise Price Option
  Low Exercise Price Option
  In 1995 the Australian Stock Exchange started listing of new exchange traded option product called a Low Exercise Price Option . A LEPO is a European style call option with a low exercise price of $0.01 and a contract size of 1000 shares to be delivered on exercise.LEPOs are traded on margin...
  
  (LEPO) is a European style call option with a low exercise price of $0.01.

Non-vanilla path dependent "exotic" options

The following "exotic option

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....

s" are still options, but have payoffs calculated quite differently from those above. Although these instruments are far more unusual they can also vary in exercise style (at least theoretically) between European and American:

• A lookback option is a path dependent
  Path dependence
  Path dependence explains how the set of decisions one faces for any given circumstance is limited by the decisions one has made in the past, even though past circumstances may no longer be relevant....
  
   option where the option owner has the right to buy (sell) the underlying instrument at its lowest (highest) price over some preceding period.

• An Asian option
  Asian option
  An Asian option is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some pre-set period of time...
  
  (or Average option) is an option where the payoff is not determined by the underlying price at maturity but by the average underlying price over some pre-set period of time. For example an Asian call option might pay MAX(DAILY_AVERAGE_OVER_LAST_THREE_MONTHS(S) - K, 0). Asian options were originated in Asian markets to prevent option traders from attempting to manipulate the price of the underlying security on the exercise date.

• A Russian option is a lookback option which runs for perpetuity. That is, there is no end to the period into which the owner can look back.

• A game option or Israeli option is an option where the writer has the opportunity to cancel the option he has offered, but must pay the payoff at that point plus a penalty fee.

• The payoff of a Cumulative Parisian option is dependent on the total amount of time the underlying asset value has spent above or below a strike price.

• The payoff of a Standard Parisian option is dependent on the maximum amount of time the underlying asset value has spent consecutively above or below a strike price.

• A barrier option involves a mechanism where if a 'limit price' is crossed by the underlying, the option either can be exercised or can no longer be exercised.

• A double barrier option involves a mechanism where if either of two 'limit prices' is crossed by the underlying, the option either can be exercised or can no longer be exercised.

• A Cumulative Parisian barrier option involves a mechanism where if the total amount of time the underlying asset value has spent above or below a 'limit price', the option can be exercised or can no longer be exercised.

• A Standard Parisian barrier option involves a mechanism where if the maximum amount of time the underlying asset value has spent consecutively above or below a 'limit price', the option can be exercised or can no longer be exercised.

• A reoption occurs when a contract has expired without having been exercised. The owner of the underlying security may then reoption the security.

• A binary option
  Binary option
  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...
  
  (also known as a digital option) pays a fixed amount, or nothing at all, depending on the price of the underlying instrument at maturity.

• A chooser option
  Chooser option
  A chooser option is a special type of option contract. It gives the purchaser a fixed period of time to decide whether the derivative will be a European call or put option....
  
  gives the purchaser a fixed period of time to decide whether the derivative will be a vanilla call or put.

• A forward start option is an option whose strike price is determined in the future

• A cliquet option is a sequence of forward start options

Related

• Covered call
  Covered call
  A covered call is a financial market transaction in which the seller of call options owns the corresponding amount of the underlying instrument, such as shares of a stock or other securities. If a trader buys the underlying instrument at the same time as he sells the call, the strategy is often...
  
  
• Moneyness
  Moneyness
  In finance, moneyness is a measure of the degree to which a derivative is likely to have positive monetary value at its expiration, in the risk-neutral measure. It can be measured in percentage probability, or in standard deviations....
  
  
• Naked put
  Naked put
  A naked put is a put option where the option writer does not have a position in the underlying stock or other instrument. This strategy is best used by investors who want to accumulate a position in the underlying stock - but only if the price is low enough...
  
  
• Option (finance)
  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...
  
  
• Option time value
  Option time value
  In finance, the time value of an option is the premium a rational investor would pay over its current exercise value , based on its potential to increase in value before expiring. This probability is always greater than zero, thus an option is always worth more than its current exercise value...
  
  
• 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...
  
  
• Put-call parity

See also

• CBOE
• Derivative (finance)
  Derivative (finance)
  A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...
  
  
• Derivatives market
  Derivatives market
  The derivatives market is the financial market for derivatives, financial instruments like futures contracts or options, which are derived from other forms of assets....
  
  s
• Financial economics
  Financial economics
  Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....
  
  
• Financial instruments
  Financial instruments
  A financial instrument is a tradable asset of any kind, either cash; evidence of an ownership interest in an entity; or a contractual right to receive, or deliver, cash or another financial instrument....
  
  , Finance
  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...
  
  
• Futures contract
  Futures contract
  In finance, a futures contract is a standardized contract between two parties to exchange a specified asset of standardized quantity and quality for a price agreed today with delivery occurring at a specified future date, the delivery date. The contracts are traded on a futures exchange...
  
  s
• Option screener
  Option screener
  An option screener is a tool that evaluates options based on criteria and generates a list of potential trading ideas. Most people who trade options are technical traders. It essentially means they look for patterns in charts. Also they use statistical correlations and deviations and give them...
  
  s
• Monte Carlo methods in finance
  Monte Carlo methods in finance
  Monte Carlo methods are used in finance and mathematical finance to value and analyze instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining their average value over the range of resultant outcomes. This is usually done...
  
  

Options

• Binary option
  Binary option
  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...
  
  
• Bond option
  Bond option
  In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC....
  
  
• Credit default option
  Credit default option
  In finance, a default option, credit default swaption or credit default option is an option to buy protection or sell protection as a credit default swap on a specific reference credit with a specific maturity...
  
  
• Exotic interest rate option
• Foreign exchange option
  Foreign exchange option
  In finance, a foreign-exchange option is a derivative financial instrument that gives the owner the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date.The FX options market is the deepest, largest and...
  
  
• Interest rate cap and floor
  Interest rate cap and floor
  An interest rate cap is a derivative in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed strike price...
  
  
• Options on futures
• Rainbow option
  Rainbow option
  Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. Rainbow options are usually calls or puts on the best or worst of n underlying assets, or options which...
  
  
• Real option
  Real option
  Real options valuation, also often termed Real options analysis, applies option valuation techniques to capital budgeting decisions. A real option itself, is the right — but not the obligation — to undertake some business decision; typically the option to make, abandon, expand, or contract a...
  
  
• Stock option
• Swaption
  Swaption
  A swaption is an option granting its owner the right but not the obligation to enter into an underlying swap. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swaps....
  
  
• Warrant
  Warrant (finance)
  In finance, a warrant is a security that entitles the holder to buy the underlying stock of the issuing company at a fixed exercise price until the expiry date....
  
  

External links

• option types data base, global-derivatives.com
• Varieties of programming codes on option valuation