Below are given the "exotic options" that are still options, but they have payoffs calculated quite differently from those that I have mentioned in my previous post. Although these instruments are far more unusual and they can also show variations in exercise style (at least theoretically) between European and American:

Lookback Option

A path dependent option where the option owner is given the right to buy (sell) the underlying instrument at its lowest (highest) price over some preceding period is referred to as a lookback option.

Asian Option

An option where the payoff is not determined by the underlying price at maturity but rather than that it is determined by the average underlying price over some pre-set period of time. For instance an MAX(DAILY_AVERAGE_OVER_LAST_THREE_MONTHS(S) – K, 0) might be paid by Asian call option.

The origin of Asian options are the Asian markets. They have been originated in order to prevent option traders from attempting to manipulate the price of the underlying security on the exercise date.

Russian Option

A lookback option which runs for perpetuity is referred to as a Russian option. What it means is that, there is no end to that period into which the owner can look back.

Game Option or Israeli Option

An option is referred to as a game option or Israeli option in which the writer has been provided the opportunity to cancel the option he has offered, but doing that he must have to pay the payoff at that point in addition to this he also has to pay a penalty fee.

Cumulative Parisian Option

Cumulative Parisian option is an option in which the payoff is dependent on the total amount of time that has been spent above or below a strike price by the underlying asset value.

Standard Parisian Option

Standard Parisian option is an option in which the payoff is dependent on the maximum amount of time has been spent consecutively above or below a strike price by the underlying asset value.

Barrier Option

A barrier option is referred to as an option that involves a mechanism where if the underlying has crossed a ‘limit price’ then the option either can be exercised or it can no longer be exercised.

Double Barrier Option

A double barrier option is referred to as an option that involves a mechanism where if the underlying has crossed either of two ‘limit prices’ then the option either can be exercised or can no longer be exercised.

Cumulative Parisian Barrier Option

An option is referred to as Cumulative Parisian barrier option if it 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.

Standard Parisian Barrier Option

An option is referred to as Standard Parisian barrier option if it involves a mechanism where if the maximum amount of time the underlying asset value has spent consecutively above or below a ‘limit price’, then the option can be exercised or can no longer be exercised.

Reoption

A reoption takes place if in case a contract has expired without having been exercised. The owner of the underlying security may then decide to reoption the security. The term and strike price of the new option may be the same as or it might have some difference from the original option.

Binary Option

A fixed amount is paid by a binary option which is also known as a digital option, or it may pay nothing at all, that depends on the price of the underlying instrument at maturity.

Chooser Option

By a chooser option the purchaser is given a fixed period of time in order to decide whether the derivative will be a vanilla call or put.

Forward Start Option

A forward start option is name given to an option whose strike price is determined in the future.

Cliquet Option

A cliquet option is a name given to a sequence of forward start options.

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