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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

Which of the following is the main reason why an American put option on a non-dividend-paying share may be exercised early?

An American put may be exercised early because, when the share price is deep in the money, the payoff is nearly at its maximum, so further gain from waiting is small. Receiving the strike now and earning interest on it outweighs the remaining time value.

  1. AExercising early gives the strike immediately, which can be invested at the risk-free rate, and the remaining upside from waiting is small when the share price is very lowCorrect
  2. BExercising early avoids the dividend payment on the share
  3. CExercising early removes the volatility risk of the share price falling further
  4. DExercising early is always optimal when the put is at the money
  5. Exercising early lets the holder benefit from rising share prices

Explanation

When the share price is very low, the put's payoff K - S is close to its maximum K. Waiting adds little extra payoff but delays receipt of cash K, which loses interest. Early exercise can therefore be optimal. The other options misdescribe the put payoff or the dividend role.

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