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FRM Part I · FRM Exam Part I · Options Markets

A trader compares two American call options on the same non-dividend-paying stock with identical strikes, one expiring in three months and the other in nine months. Which statement is correct?

The nine-month American call is worth at least as much as the three-month call, because it carries every exercise right of the shorter option plus additional time. A longer-lived American option can never be worth less than an otherwise identical shorter-lived one.

  1. AThe nine-month call is worth at least as much as the three-month callCorrect
  2. BThe three-month call is worth more because of faster time decay
  3. CThe two calls must have the same value because early exercise is never optimal
  4. DThe nine-month call is worth less because of greater discounting of the strike

Explanation

An American option with a longer life gives the holder all the rights of the shorter option plus more, so it cannot be worth less. Time decay does not make the shorter option more valuable. Equal value would hold only in degenerate cases.

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