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

A trader holds an American call option on a non-dividend-paying stock. Which statement about early exercise of this call before expiry is correct?

Early exercise of an American call on a non-dividend-paying stock is never optimal. Its value is at least S - K discounted, which exceeds S - K, so exercising early forfeits time value, interest on the strike and downside protection. Selling the option is always better than exercising.

  1. AIt is never optimal, because the call's value exceeds its immediate exercise value (S - K) while interest can be earned on the strike and the option's insurance value is retainedCorrect
  2. BIt is always optimal when the option is deep in the money
  3. CIt is optimal whenever interest rates are positive
  4. DIt is optimal immediately before expiry only if the stock volatility is high

Explanation

For a non-dividend-paying stock, the European call value satisfies c >= S - K*e^(-rT) > S - K for r > 0. An American call is worth at least as much as the European call, so exercising early would sacrifice value. Deep in-the-money status alone does not justify exercise, because selling the option realizes more than exercising.

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