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FRM Part I · FRM Exam Part I · Exotic Options

A European down-and-in call and a European down-and-out call have the same underlying, strike, barrier and expiry, and the barrier is below the initial stock price. The down-and-out call is worth 4.10 and the standard European call is worth 9.35. What is the value of the down-and-in call?

The down-and-in call is worth 5.25. In-out parity states that a knock-in option plus an otherwise identical knock-out option equals the vanilla option, so 9.35 minus 4.10 gives 5.25.

  1. A5.25Correct
  2. B13.45
  3. C4.10
  4. D9.35

Explanation

In-out parity says knock-in plus knock-out equals the vanilla option. Down-and-in = 9.35 - 4.10 = 5.25. The sum 13.45 wrongly adds the vanilla and knock-out values.

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