Consider the following at-the-money options, all of the same maturity: a vanilla European call ( $C _ { E }$ ), an American vanilla call ( $C _ { A }$ ), a fixed-strike lookback call ( $C _ { L }$ ). Which of the following is correct?
A) $C _ { L } \leq C _ { E } \leq C _ { A }$
B) $C _ { L } \leq C _ { E } \leq C _ { A }$.
C) $C _ { E } \leq C _ { A } \leq C _ { L }$
D) $C _ { A } \leq C _ { E } \leq C _ { L }$.

Question

Quizplus · Accepted Answer

Fixed-strike lookback options ( $C _ { L }$ ) are more expensive than vanilla options because they offer the maximum payoff from the best stock price achieved during the option's life. American options ( $C _ { A }$ ) can be more valuable than European options ( $C _ { E }$ ) because they can be exercised at any time before expiration, potentially capturing more value. Therefore, $C _ { E } \leq C _ { A } \leq C _ { L }$ is the correct ordering.

Consider the Following At-The-Money Options, All of the Same Maturity CEC _ { E }CE​

Consider the Following At-The-Money Options, All of the Same Maturity $C _ { E }$