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

An analyst values an American call on a stock that pays no dividends during the option's life. The call is deep in the money with several months to expiry. Which statement about early exercise is correct?

Early exercise of an American call on a non-dividend-paying stock is never optimal. The call is worth more than its intrinsic value, since delaying payment of the strike earns interest and the option still protects against price falls. Exercising early surrenders both benefits.

  1. AEarly exercise is never optimal, because exercising forfeits the option's time value and the interest that could be earned on the strikeCorrect
  2. BEarly exercise is optimal whenever the call is deep in the money, because intrinsic value is then locked in
  3. CEarly exercise is optimal when interest rates are high, because the strike payment is then discounted more heavily
  4. DEarly exercise is optimal only in the final month, because time value is then negligible

Explanation

For a non-dividend-paying stock, an American call is worth at least S0 - K*exp(-rT), which exceeds S0 - K while rates are positive and T > 0. Selling the option therefore beats exercising it. Exercising early also means paying the strike sooner and giving up the protection against a price fall. Waiting until expiry costs nothing extra.

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