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FRM Part I · FRM Exam Part I · Introduction to Derivatives

Which statement about the payoff at expiration of a long position in a European put option with strike K and final stock price S is correct?

A long put pays max(K minus S, 0) at expiration. It is never negative because the holder may decline to exercise, and since the stock price cannot go below zero, the payoff is capped at the strike price K.

  1. AIt equals max(K - S, 0) and is bounded above by KCorrect
  2. BIt equals max(S - K, 0) and is unbounded above
  3. CIt equals min(K - S, 0) and is bounded below by -K
  4. DIt equals K - S and can be negative without limit

Explanation

A put holder gains only when S is below K, so payoff is max(K - S, 0). Since S cannot fall below zero, the maximum payoff is K. The other options describe a call payoff, or an obligation that a long option holder does not have.

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