Option style

In finance, the style or family of an option is 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 (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 options". Exotic options can pose challenging problems in valuation and hedging.

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 expiration 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 expiration date.

For both, the payoff—when it occurs—is given by

max

{

(

S

−

K

)

,

0

}

{\displaystyle \max\{(S-K),0\}}

, for a call option

max

{

(

K

−

S

)

,

0

}

{\displaystyle \max\{(K-S),0\}}

, for a put option

where

K

{\displaystyle K}

is the strike price and

S

{\displaystyle S}

is the spot price of the underlying asset.

Option contracts traded on futures exchanges are mainly American-style, whereas those traded over-the-counter are mainly European.