Question

American options will be valued at least as large as European options. Exercising early will increase its value relative to the European option, except when the option does not pay dividends

a. true
b. false

Answer 1

The statement is **true**.

In options trading, American options grant the holder the right to exercise the option at any time before its expiration date, while European options can only be exercised at the expiration date. Therefore, American options provide more flexibility to the holder, potentially leading to a higher value compared to European options.

Exercising an American option early can increase its value relative to a European option under certain circumstances, especially when the underlying asset pays dividends. By exercising early, the option holder can benefit from receiving dividends sooner, which increases the option's value. However, if the underlying asset does not pay dividends, the advantage of early exercise diminishes, and both American and European options may have similar values.

Hence, the statement is true, specifying that American options will generally be valued at least as large as European options, and early exercise can increase its value, except when the underlying asset does not pay dividends.

Answer 2

The statement is generally true, with American options being at least as valuable as European options due to the flexibility to exercise early, especially if the assets pay dividends. Without dividends, the advantage of American options diminishes as early exercise becomes less beneficial.

Step-by-step explanation:

The statement 'American options will be valued at least as large as European options. Exercising early will increase its value relative to the European option, except when the option does not pay dividends' is generally true. American options provide the holder with the right to exercise the option at any time up to and including the expiration date, which adds potential value since it allows for earlier access to potential profits, particularly if the assets pay dividends. This is in contrast to European options, which can only be exercised at maturity.

However, if the underlying asset does not pay dividends, the incentive to exercise early lessens, and the value difference between an American option and a European option may be negligible. Without dividends, the potential financial advantages of early exercise, such as securing dividends or reinvesting at a higher rate, are eliminated. Thus, considering time value of money and opportunity cost, holding the option to maturity could be more beneficial than early exercising.