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FRM Part I · FRM Exam Part I · Properties of Options

A trader holds an American call option on a stock that pays no dividends during the life of the option. Which statement about early exercise is correct?

Early exercise of an American call on a non-dividend-paying stock is never optimal. The option's value is at least S0 minus the discounted strike, which exceeds immediate intrinsic value S0 minus K when rates are positive, so holding or selling beats exercising.

  1. AIt is never optimal to exercise early, because the call is worth more unexercised than its intrinsic valueCorrect
  2. BIt is optimal to exercise early whenever the call is in the money
  3. CIt is optimal to exercise early whenever interest rates are positive
  4. DIt is optimal to exercise early just before expiration only if volatility is high

Explanation

For a non-dividend-paying stock, the call value satisfies c >= S0 - K*exp(-rT), which exceeds S0 - K when r > 0. Exercising early gives only S0 - K and forfeits time value and the interest benefit of deferring payment of the strike. Selling the option is always better than exercising it early.

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