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FRM Part I · FRM Exam Part I · Properties of Options

Which statement about the relationship between American and European options on the same non-dividend-paying stock, with the same strike and expiry, is correct?

The American put is worth at least as much as the European put, because early exercise can be valuable for puts. The American call equals the European call on a non-dividend-paying stock, since early exercise of such a call is never optimal and the extra right adds no value.

  1. AAn American put is worth at least as much as the European put, and the American call equals the European callCorrect
  2. BAn American call is worth strictly more than the European call
  3. CAn American put is always worth exactly the same as the European put
  4. DAn American call is worth less than the European call because of early exercise costs

Explanation

An American option has all the rights of a European option plus early exercise, so it is worth at least as much. For calls on non-dividend stock, early exercise is never optimal, so the extra right has no value and C = c. For puts, early exercise can be optimal, so P >= p, with strict inequality possible.

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