Different styles of options include European, American, Bermudan, Barrier, Exotic and Vanilla options (a vanilla option being any option that is not exotic).
American and European options
European options may only be exercised on their expiration date, while American options can be exercised on or before that date. American options expire on the third Saturday of every month and are closed for trading the Friday before, while European ones expire the third Friday of every month and are closed for trading on the Thursday before.
For both styles, the pay-off is calculated as:
The maximum of the strike price minus the spot price or zero, for a call
The maximum of the spot price minus strike price or zero, for a put
Where an American and European option are otherwise identical (having the same strike price, etc.), the American one will be worth at least as much as the European one. If it is worth more, the difference in value can be used to determine whether or not it should be exercised before the expiration date.
Options contracts traded on exchanges are mainly American, whereas options traded over the counter are mainly European.
A Bermudan option may be exercised on specific dates on or before expiration. It is half-way between European (which allow exercise at one time) and American (which allow exercise at any time) options. Most exotic interest rate options are Bermudan style options.
Barrier options can only be exercised once the underlying asset’s price has passed a certain level, or barrier. Barriers are always cheaper than non-barriers, and were created to allow investors to hedge with options without having to pay as high a premium.
The two types of barrier options are ‘in’ and ‘out’ options – ‘in’ options start their lives worthless and become active when a set barrier is reached, while ‘out’ options start their lives active and become worthless once a barrier is broken. Both types can be divided into two more categories – up-and-out or down-and-out, or up-and-in and down-and-in.
• Up-and-out: the spot price starts below the barrier and has to rise for the option to expire
• Down-and-out: the spot price starts above the barrier level and has to fall for the option to expire
• Up-and-in: the spot price starts below the barrier level and has to rise for the option to become activated
• Down-and-in: the spot price starts above the barrier level and has to fall for the option to become activated
Exotic options can have both standard and non-standard exercise styles, as well as standard and non-standard pay-off calculations.
Exotics with standard exercise styles can be exercised either in the European or American style, the only difference being the calculation of their pay-off value:
• A cross option is on an asset in one currency with a strike price denominated in another currency – one example would be IBM, which is denominated in US dollars. Trading on IBM in Japan would involve converting the pay-off into Japanese Yen, meaning the pricing of these options needs to take forex volatility into account. A quanto option is another version of this, but the exchange rate is set from the outset of the trade.
• An exchange option is the right to exchange one asset for another.
• A basket option is on the weighted average of several underlying assets. A rainbow option is a basket option where the weighting depends on the financial performance of each asset.
• A low exercise price option is a European call option with a low exercise price of USD0.01.
Some exotic options can use the same pay-off values as American and European options, but the early exercise can occur differently:
• A Canary option has exercise styles between European options and Bermudan options – typically the holder can exercise the option at quarterly dates, but not before a set time period (usually 12 months) has passed.
• A capped-style option has a profit cap written into the contract – capped-style options are automatically exercised when the underlying asset reaches that price.
• A compound option is an option on an option, giving the holder two separate exercise dates and decisions.
• A shout option allows the holder two exercise dates – before the expiration date the holder can ‘shout’ to the seller that they want to lock-in the current price, and if this gives them a better deal than the ay-off at maturity they can use the shout date price rather than the price at maturity to calculate the pay-off.
• A swing option gives the holder the right to exercise only one call or put on any one of a number of specified exercise dates, with penalties imposed with the holder has a net volume higher or lower than specified upper or lower limits.
Other exotics have pay-offs that are calculated quite differently, alongside their exercise styles varying:
• A look-back option is where the holder has the right to buy or sell an underlying asset at its lowest or highest price over a preceding period, while a Russian option is a type of look-back option that has an infinite preceding period.
• An Asian (or average) option’s payoff is determined by the average price of the underlying asset over a predetermined period of time.
• A game (or Israeli) option is where the writer can cancel the option offered, but must pay that point’s pay-off as well as a penalty fee.
• A cumulative Parisian option has a pay-off dependent on the total amount of time the underlying asset value is above or below a certain strike price, while a standard Parisian option is dependent on the maximum amount of time the underlying asset value spent consecutively above or below a strike price.
• A re-option occurs when a contract has expired without having been exercised, and the owner of the underlying asset may then re-option the asset.
• A binary (or digital) option pays a fixed amount, or nothing at all, depending on the price of the underlying asset at maturity.
• A forward start option is an option with a strike price to be determined in the future, and a cliquet option is a sequence of forward starts.