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IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model

In a binomial tree model for a non-dividend-paying share, which statement about an American call option on that share is correct?

An American call on a non-dividend-paying share is never exercised early, because holding it is worth more than exercising it. Its value therefore equals the European call's value, and the early exercise right adds nothing.

  1. AIt is never optimal to exercise early, so its value equals that of the otherwise identical European callCorrect
  2. BIt should always be exercised at the first node where it is in the money
  3. CIt is worth strictly more than the European call because of the early exercise right
  4. DIt should be exercised early whenever the risk-free rate is positive
  5. It is worth less than the European call because of the early exercise right

Explanation

For a non-dividend-paying share, the call's value before expiry is at least S minus the discounted strike, which exceeds the intrinsic value S minus K when rates are positive. Early exercise is therefore never optimal, and the American and European calls have equal value. The claim that the American call is worth more is wrong because the extra right has no value here.

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