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

A non-dividend-paying stock underlies an American call option and an otherwise identical European call option. Which statement is correct?

The American call on a non-dividend-paying stock should never be exercised early, because exercising gives up time value and interest on the strike. Its early exercise right is worthless, so its value equals that of the European call.

  1. AThe American call should never be exercised early, so its value equals the European call valueCorrect
  2. BThe American call is always worth strictly more than the European call because of the early exercise right
  3. CThe American call should be exercised just before expiration only if the stock price is below the strike
  4. DThe American call should be exercised early whenever it is deep in the money to lock in intrinsic value

Explanation

For a non-dividend-paying stock, a call's value before expiry exceeds its intrinsic value, because exercising early forfeits the time value and the interest earned on the strike. Selling the option or holding it is therefore better than exercising. Hence the early exercise right has no value and the American and European calls are worth the same.

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