FRM Part I · FRM Exam Part I · Exotic Options
A European up-and-in call and an up-and-out call share the same strike, maturity and barrier on the same underlying. The vanilla European call with the same strike and maturity is worth USD 8.40, and the up-and-out call is worth USD 3.15. Using in-out parity, what is the value of the up-and-in call?
By in-out parity, a knock-in plus a knock-out with identical terms equals the vanilla option. The up-and-in call is therefore 8.40 minus 3.15, which equals USD 5.25. Adding the values would wrongly give 11.55, exceeding the vanilla price.
- AUSD 5.25Correct
- BUSD 11.55
- CUSD 3.15
- DUSD 8.40
Explanation
In-out parity: knock-in + knock-out = vanilla. So up-and-in = 8.40 - 3.15 = 5.25. The 11.55 option wrongly adds the two values. The 3.15 and 8.40 options simply repeat given values.
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