American Derivative Securities
European option contracts specify an expiration date, and if the option is to be exercised, the exercise must occur on the expiration date. An option whose owner can choose to exercise at any time up to and including the expiration date, or to not exercise at all, is called American. Because of this early exercise feature, such an option is at least as valuable as its European counterpart. Sometimes the difference in value is negligible or even zero, and then American and European options are close or exact substitutes. We shall see in this chapter that the early exercise feature for a call on a stock paying no dividend is worthless; American and European calls have the same price. In other cases, most notably put options, the value of this early exercise feature, the so-called early exercise premium, can be substantial. An intermediate option between American and European is Bermudan, an option that permits early exercise but only on a contractually specified finite set of dates.
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