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Which of the following options is the most valuable?
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.
Was this the correct answer/reasoning? What do you think?
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.
