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

Which statement about upper bounds on option prices for a non-dividend-paying stock is correct?

An American put is capped at the strike K, and a European put at the present value of K, because the best possible payoff is K when the stock falls to zero. Calls are capped at the stock price.

  1. AAn American put can never be worth more than the strike price K, and a European put can never be worth more than the present value of KCorrect
  2. BA European call can be worth more than the stock price if volatility is high
  3. CA European put can be worth more than K if the stock price falls to zero
  4. DAn American call can be worth more than the stock price if interest rates are high

Explanation

A call gives the right to buy one share, so it can never exceed the stock price, whatever the volatility or rates. The maximum payoff of a put is K (when the stock goes to zero), so an American put is bounded by K and a European put, paid only at expiry, by K e^(-rT). The other statements violate these bounds.

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