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FRM Part I · FRM Exam Part I · Exotic Options

Compared with a standard European put with the same strike and maturity, an up-and-out put whose barrier is set well above the current spot price will most likely be:

It will be slightly cheaper than the standard put. Hitting a high barrier requires a price rise, when the put is least valuable, so knock-out removes only a small portion of value from paths that rise to the barrier and later fall.

  1. ASlightly cheaper, because a rise to the barrier is unlikely and the put is out of the money then anywayCorrect
  2. BMuch more expensive, because knock-outs carry a premium
  3. CWorth exactly the same, since put payoffs are unaffected by barriers
  4. DWorth zero at inception because the barrier is above spot

Explanation

A put gains value when the price falls, so paths hitting a high barrier are those where the put is least valuable. Knocking out removes little value and the up-and-out put is only slightly cheaper than the vanilla put. It is not identical, since some value is lost on paths that rise then fall.

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