An option gives its purchaser the right to buy (call ) or sell (put ) a specified underlying at a fixed price (strike ) at (European ) or up to (American ) a fixed date (maturity ). In the age of exotic options, this traditional definition is no longer sufficient. In order to include the “exotics”, this definition requires generalization: an option on one or several underlyings with prices given by S 1, S 2, ...Sm is characterized by its payoff profile. The payoff of the option is a function F (S 1, S 2, ...Sm ) of the underlying prices and indicates the cash flows arising for the option’s holder upon exercise1. American options can be exercised at any time during the lifetime of the option in contrast to the European option, which can only be exercised at maturity. There are also options which can be exercised at several specific times during their lifetime. These are called Bermuda options or Atlantic options since, in a sense, they are an intermediate form between American (exercise is possible at any time during the option’s lifetime) and European (exercise is possible at a single time, namely at maturity) options.
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