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

Under the Black-Scholes-Merton framework extended to American options on a non-dividend-paying stock, which statement is correct about early exercise of an American call option?

The American call on a non-dividend-paying stock is never exercised early, so it equals the European call. Early exercise gives up time value, interest on the strike and downside protection, and the option's value exceeds its intrinsic value S minus K, so selling is better.

  1. AIt is never optimal to exercise early, so the American call has the same value as the European callCorrect
  2. BIt is optimal to exercise early whenever the call is deep in the money
  3. CIt is optimal to exercise early just before maturity if interest rates are positive
  4. DIt is optimal to exercise early whenever volatility is low

Explanation

Exercising early forfeits the time value and the interest earned on the strike, and gives up the insurance value of the option. The call's value is always at least S - K*exp(-rT), which exceeds S - K, so selling the call beats exercising. Hence the American and European calls have equal value.

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