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FRM Part I · FRM Exam Part I · Exotic Options

Consider two European options on the same stock with the same strike and maturity: a standard call and a down-and-out call with a barrier below the current price. Which statement is correct?

The down-and-out call is worth no more than the standard call. It has the same payoff when it survives but can be cancelled if the barrier is hit, so it can only be cheaper or equal. The buyer's loss remains limited to the premium.

  1. AThe down-and-out call is worth no more than the standard callCorrect
  2. BThe down-and-out call is worth more than the standard call because it can be knocked out
  3. CThe two have equal value if the barrier is below the strike
  4. DThe down-and-out call has unlimited downside to the buyer

Explanation

A knock-out option can only lose value relative to the vanilla option, since it can be extinguished before expiry and otherwise pays the same. So its value is at most that of the standard call. The buyer's loss is still limited to the premium.

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