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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

Which statement about early exercise of an American put on a non-dividend-paying stock is correct?

Early exercise of an American put can be optimal when it is deep in the money, because receiving the strike now earns interest and the remaining upside is limited since the stock cannot fall below zero.

  1. AIt is never optimal because the put's time value is always positive
  2. BIt may be optimal when the put is sufficiently deep in the money, because the interest earned on the strike received can outweigh the remaining insurance valueCorrect
  3. CIt is optimal only when the stock price is above the strike
  4. DIt is optimal only when interest rates are zero

Explanation

Exercising a deep in-the-money put gives the strike immediately, which can earn interest. The maximum gain is capped at K, so waiting adds little upside, while the forgone interest is a real cost. At zero rates early exercise would not be beneficial, and exercise above the strike is pointless.

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