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

Under the Black-Scholes-Merton framework, a trader holds an American call option on a stock that pays no dividends during the option's life. Which statement about early exercise is correct?

For a non-dividend-paying stock, an American call should never be exercised early because exercising gives up time value, interest on the strike and downside protection. Its value therefore equals that of the European call with the same terms.

  1. AIt is never optimal to exercise early, so the American call has the same value as the otherwise identical European callCorrect
  2. BIt is optimal to exercise early whenever the option is deep in the money
  3. CIt is optimal to exercise just before expiry only if interest rates are zero
  4. DIt is optimal to exercise early when volatility is high because time value is lost

Explanation

Exercising early forgoes the time value of the option and the interest earned on the strike, and gives up the insurance value. The call's value always exceeds S - K, so selling is better than exercising. Hence the American call equals the European call when no dividends are paid. Deep in the money alone does not justify early exercise.

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