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:

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

where is the strike price and 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.

Most stock and equity options are American options, while indexes are generally represented by European options. Commodity options can be either style.

Expiration date

Traditional monthly American options expire the third Saturday of every month (or the third Friday if the first of the month begins on a Saturday). They are closed for trading the Friday prior.

European options traditionally 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

Assuming an arbitrage-free market, a partial differential equation known as the Black-Scholes equation can be derived to describe the prices of derivative securities as a function of few parameters. Under simplifying assumptions of the widely adopted Black model, the Black-Scholes equation for European options has a closed-form solution known as the Black-Scholes formula. In general, no corresponding formula exist for American options, but a choice of methods to approximate the price are available (for example Roll-Geske-Whaley, Barone-Adesi and Whaley, Bjerksund and Stensland, binomial options model by Cox-Ross-Rubinstein, Black's approximation and others; there is no consensus on which is preferable).[1] Obtaining a general formula for American options without assuming constant volatility is one of finance's unsolved problems.

An investor holding an American-style option and seeking optimal value will only exercise it before maturity under certain circumstances. Owners who wish to realise the full value of their option will mostly prefer to sell it as late as possible, rather than exercise it immediately, which sacrifices the time value. See early exercise consideration for a discussion of when it makes sense to exercise early.

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

Less common exercise rights

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

Bermudan option

Canary option

Capped-style option

Compound option

Shout option

Double option

Swing option

Evergreen option

"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 payoff value:

Composite option

Quanto option

Exchange option

Basket option

Rainbow option

Low Exercise Price Option

Boston option

Non-vanilla path-dependent "exotic" options

The following "exotic options" 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:

Lookback option

Asian option

Game option

Cumulative Parisian option

Standard Parisian option

Barrier option

Double barrier option

Cumulative Parisian barrier option

Standard Parisian barrier option


Binary option

Chooser option

Forward start option

Cliquet option

See also




  1. ^ "". Retrieved 12 April 2018.
  2. ^[bare URL PDF]
  3. ^ Gooley, Nathan John (2015), Evergreen, bank funding & liquidity management, Pg 204-5: University of Newcastle, hdl:1959.13/1310643((citation)): CS1 maint: location (link)
  4. ^ Rogers, L.C.G.; Shi, Z. (1995), "The Value of an Asian Option" (PDF), Journal of Applied Probability, 32 (4): 1077–1088, doi:10.2307/3215221, JSTOR 3215221, S2CID 120793076, archived from the original (PDF) on 2009-03-20, retrieved 2008-11-15
  5. ^ Paul Wilmott (25 October 2013). "Chapter 25 section 25.1". Paul Wilmott on Quantitative Finance. John Wiley & Sons. ISBN 978-1-118-83683-5.
  6. ^ Kifer, Yuri (2000). "Game options". Finance and Stochastics. 4 (4): 443–463. doi:10.1007/PL00013527. S2CID 32671470.