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

Which statement about American and European options on a non-dividend-paying share is correct under no-arbitrage?

An American call on a non-dividend share has the same value as the European call. Its value before expiry exceeds its intrinsic value, so exercising early forfeits time value and is never optimal. American puts, by contrast, can be worth more.

  1. AAn American call should always be exercised early because of time value of money
  2. BAn American call is worth strictly more than an otherwise identical European call
  3. CAn American call has the same value as an otherwise identical European call, since early exercise is never optimalCorrect
  4. DAn American put is always worth the same as a European put
  5. A European call can be worth more than the share price

Explanation

Before expiry the call's value exceeds S - K, so selling it beats exercising; early exercise is never optimal, making American and European calls equal in value. Puts can be optimally exercised early, so American puts can exceed European ones. A call can never exceed the share price.

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