FRM Part I · FRM Exam Part I · Exotic Options
A European call on a non-dividend stock is worth 8.00. A down-and-out call with the same strike, maturity, and a barrier below the current spot is worth 5.50. What is the value of the otherwise identical down-and-in call?
The down-and-in call is worth 2.50. A knock-in and a knock-out with identical terms together replicate the vanilla call, so the knock-in equals the vanilla value of 8.00 minus the knock-out value of 5.50.
- A2.50Correct
- B5.50
- C8.00
- D13.50
Explanation
In-out parity says a knock-in plus a knock-out with identical terms replicates the vanilla option, because exactly one of them is alive at maturity. So the down-and-in call = 8.00 − 5.50 = 2.50. Adding the values (13.50) is a sign error.
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