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FRM Part I · FRM Exam Part I · Binomial Trees

A risk analyst values an American call option on a stock that pays no dividends, using a binomial tree. Which statement about early exercise at interior nodes is correct?

Early exercise of an American call on a non-dividend-paying stock is never optimal. Exercising early gives up the option's time value and the interest that could be earned on the strike. The American call is therefore worth the same as the equivalent European call.

  1. AEarly exercise is never optimal, because exercising forfeits the option's remaining time value and the interest earned on the deferred strike paymentCorrect
  2. BEarly exercise is optimal whenever the option is in the money, because the intrinsic value is locked in
  3. CEarly exercise is optimal at the final step before expiry only if the up-move probability exceeds 0.5
  4. DEarly exercise is optimal when interest rates are high, because the strike can be paid later at a lower present value

Explanation

For a non-dividend-paying stock, the call is always worth at least S minus the discounted strike, which exceeds S minus K. Exercising early gives up the time value and the interest on the strike, so it is never optimal. The American call therefore has the same value as the European call. The last option confuses cause and effect: high rates make waiting more valuable for a call, not less.

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