Final answer:
American options, which can be exercised any time before expiration, are generally valued higher than European options, which can only be exercised on the expiration date. This flexibility in exercise timing means American options are valued at least as large, and typically higher, than their European counterparts, even when no dividends are paid.
Step-by-step explanation:
When comparing American options to European options, it is important to note that American options can be exercised at any time up to the expiration date, whereas European options can only be exercised at the expiration date. Due to this flexibility, American options are typically valued at least as large as their European counterparts. However, if the option does not pay dividends, the advantage of exercising early disappears, as the benefit of holding the option usually outweighs the advantage of exercising it early due to the time value of money.
Therefore, the answer to the question whether American options will be valued equally, higher, or lower than European options when not paying dividends is B. Valued higher. This is because even without dividends, the mere possibility of early exercise can enhance the American option's value over the European option, even though in practice early exercise might not always increase value.