Final answer:
The statement is true; American options are more complex than European options as they can be exercised at any point during their life, adding to valuation difficulties.
Step-by-step explanation:
The statement that American options are more complex than European options because they can be exercised at any time during the life of the option is true. American options offer the holder more flexibility as they allow the option to be exercised on any trading day up to and including the expiration date. This contrasts with European options, which can only be exercised at the expiration date.
The complexity in American options arises from this additional flexibility, making their valuation more complex because the option's value cannot simply be determined at a single point in time. Various factors, including the current stock price, the strike price, time to expiration, and interest rates, along with the potential for early exercise, need to be considered. This may lead investors and traders to use more sophisticated pricing models and strategies when dealing with American options.