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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

A non-dividend-paying share has a current price of Rs 500. An American call option and a European call option on it have the same strike and expiry, and interest rates are positive. Which statement about early exercise of the American call is correct?

The American call on a non-dividend-paying share should never be exercised early, because its market value exceeds its intrinsic value. Deferring payment of the strike earns interest and retains optionality, so the American call is worth the same as the European call.

  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 in the money
  3. CIt is optimal to exercise early only in the final week before expiry
  4. DIt is optimal to exercise early whenever the share price has risen since issue
  5. The American call is always worth strictly more than the European call

Explanation

For a non-dividend-paying share, the call's value before expiry exceeds its intrinsic value S - K because of time value and the interest earned on deferring payment of K. Selling the option beats exercising, so early exercise is never optimal. The American and European calls are therefore worth the same.

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