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, maturity and barrier (barrier below the initial spot price and below the strike). The standard European call is worth 8.40 and the down-and-out call is worth 6.15. What is the value of the down-and-in call?
The down-and-in call is worth 2.25. By in-out parity, a knock-in plus a knock-out with identical terms replicates the standard call, so the knock-in equals 8.40 minus 6.15.
- A2.25Correct
- B6.15
- C14.55
- D8.40
Explanation
In-out parity: knock-in plus knock-out equals the vanilla option. So down-and-in = 8.40 − 6.15 = 2.25. Adding the values (14.55) is a sign error that ignores parity.
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