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FRM Part I · FRM Exam Part I · Binomial Trees

A trader values an American call option on a stock that pays no dividends during the option's life, using a binomial tree. Which statement best describes the result at the tree's nodes before expiry?

Early exercise of an American call on a non-dividend-paying stock is never optimal, because the unexercised option is worth more than its intrinsic value. Exercising would forfeit time value and the interest on the strike, so the American call equals the European call.

  1. AExercise is optimal at any node where the option is in the money, because intrinsic value is locked in
  2. BThe call is worth more unexercised than its intrinsic value at every node, so early exercise is never optimal and the American call equals the European callCorrect
  3. CExercise is optimal at nodes where the stock has fallen, to avoid further losses
  4. DEarly exercise is optimal at the penultimate step because the final step adds only volatility risk

Explanation

For a non-dividend-paying stock, the call value is at least S minus the discounted strike, which exceeds S minus K whenever interest rates are positive. Exercising early gives up the time value and the interest earned on the strike. So backward induction never selects exercise, and the American call has the same value as the European call.

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