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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.

Was this the correct answer/reasoning? What do you think?

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

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    $\begingroup$ OP's ordering doesn't match yours. $\endgroup$ – Olaf Apr 15 '17 at 18:14
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    $\begingroup$ Just to be precise: The inequalities should be weak. The additional optionality might be worthless. $\endgroup$ – LocalVolatility Apr 15 '17 at 19:54
  • $\begingroup$ @LocalVolatility When? :) $\endgroup$ – Henrik Mar 29 '18 at 11:48
  • $\begingroup$ @Henrik I don't understand your comment. If you have a follow-up question then please open a new question. $\endgroup$ – LocalVolatility Mar 29 '18 at 11:51
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    $\begingroup$ 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. $\endgroup$ – LocalVolatility Mar 29 '18 at 12:40

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