# Which of the three options is the most valuable?

Which of the following options is the most valuable?

• American vanilla call
• European vanilla call
• Bermudan call

No further assumptions given - that was an interview question and I ordered them followingly:

European call < American call < Bermudan call


as the last one has the most optionalities embedded.

• Could you mark the question as answered if you feel my explanation is enough? Thanks. – Daneel Olivaw Jun 1 '17 at 13:01

The greater the optionality, the greater the price. Hence, in your case:

• a European call "gives" you optionality on a single day;

• a Bermudan call "gives" you optionality on a series of days between the beginning of the contract and its maturity;

• an American call "gives" you optionality on all days between the beginning of the contract and its maturity.

Hence your answer is not correct $-$ thank you @Olaf:

$$\textrm{American} \geq \textrm{Bermudan} \geq \textrm{European}$$

PS: Why do you think a Bermudean option has more optionality than an American one?

PS2: as precised by @LocalVolatility, the additional optionality might be worthless, hence the inequalities are not strict.

• OP's ordering doesn't match yours. – Olaf Apr 15 '17 at 18:14
• Just to be precise: The inequalities should be weak. The additional optionality might be worthless. – LocalVolatility Apr 15 '17 at 19:54
• @LocalVolatility When? :) – Henrik Mar 29 '18 at 11:48
• @Henrik I don't understand your comment. If you have a follow-up question then please open a new question. – LocalVolatility Mar 29 '18 at 11:51
• Depends on what you call degenerate. Consider a non-dividend paying stock on a geometric Brownian motion asset and assume interest rates are non-negative. Then there is no value in the additional exercise rights given by Bermudan or American call options and all three prices agree. – LocalVolatility Mar 29 '18 at 12:40