Option style

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Option style explains when you can exercise an option and how its payoff is calculated. Most options are vanilla and fall into European or American styles. Exotic options have different payoffs and can be harder to price.

Payoffs in simple terms
- The payoff depends on the strike price K and the underlying price S.
- For a standard call option, the payoff is max(S − K, 0). For a put, it’s max(K − S, 0).

American vs European
- American options can be exercised any time before they expire.
- European options can be exercised only at expiration.
- This makes American options typically more valuable than European ones, all else equal.
- Futures options are usually American; stock options are often American; indexes are usually European. Commodity options can be either.

How long they last (typical expirations)
- American options often expire on the third Saturday of the month (or Friday if the month starts on a Saturday).
- European options typically expire on the Friday before the third Saturday.
- These calendars affect when you can trade and exercise the options.

Pricing basics
- The Black-Scholes model gives a clean, exact price for European options under certain assumptions.
- There is no simple universal formula for American options. Instead, several approximation methods are used, such as Roll-Geske-Whaley, Barone-Adesi and Whaley, Bjerksund and Stensland, the binomial model, and Black’s approximation. There is no consensus on which method is best.

Early exercise and value
- An American option holder may choose to exercise before expiration if it’s beneficial, but often it’s better to hold the option to keep its time value and sell it later.
- If an American and a European option have the same terms, the American is worth at least as much. If the American price is higher, that difference reflects the value of potential early exercise.

Practical approach
- To price an American option, traders often start with the European price for the same option and then adjust for the possibility of early exercise.

Exotic options
- Exotic options have unusual payoff calculations or exercise rules. They may still be described as European or American in theory, but their payoffs differ from standard vanilla options.

In short, option style matters because it defines when you can exercise and how the payoff is determined, which in turn affects pricing and risk management.