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FRM Part I · FRM Exam Part I · Exotic Options

A trader holds a European down-and-out call option on a stock with a barrier of 80 and a strike of 100. Which statement best describes the effect of the barrier feature compared with an otherwise identical standard European call?

The down-and-out call is cheaper than the standard call. It can be extinguished if the stock touches the barrier, so the holder gives up some payoff scenarios. A knock-out option can never be worth more than the otherwise identical vanilla option.

  1. AThe option is cheaper than the standard call because it can be extinguished before expiryCorrect
  2. BThe option is more expensive than the standard call because the barrier adds protection
  3. CThe option has the same price because the barrier is below the strike
  4. DThe option is worth more only when the stock is far above the barrier

Explanation

A knock-out option gives up payoff in the scenarios where the barrier is hit, so its holder has weakly fewer payoffs than a standard call. It therefore cannot be worth more than the standard call and is generally cheaper. The barrier at 80 is below the strike, so it still has a real chance of being touched.

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