Comparing Exercise Flexibility in European, Bermudan, and American Calls

Summary

The document compares the value of otherwise comparable European, Bermudan, and American call options through their exercise rights. A European option can be exercised only at expiry, a Bermudan option on specified dates, and an American option throughout its eligible period. When one exercise schedule contains every date allowed by another, the holder has at least as much flexibility, so the American call is worth no less than the Bermudan call, which is worth no less than the European call.

The discussion corrects the questioner’s proposed ordering by pointing out that the Bermudan schedule cannot contain more exercise opportunities than the American schedule. These comparisons assume the options have otherwise matching terms and that exercise opportunities are nested. The inequalities need not be strict: extra exercise rights can have no value in some circumstances. With no further contract assumptions supplied, the post gives the general ordering rather than a numerical valuation.

Key ideas

• More available exercise dates cannot reduce an option’s value when other terms match.
• An American call allows exercise throughout its eligible period, while a Bermudan call permits exercise on specified dates.
• The general ordering is American at least Bermudan at least European.
• The value differences may be zero, so the inequalities are not necessarily strict.

Tags

# Which of the three options is the most valuable?


# 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.

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

## Answer by Daneel Olivaw (score 14)

https://quant.stackexchange.com/a/33697

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.