FRM Part I · FRM Exam Part I · Exotic Options
A cash-or-nothing call and a cash-or-nothing put have the same strike, expiry and underlying, and each pays USD 100 if in the money at expiry. The continuously compounded risk-free rate is 3% and expiry is two years. The call is worth USD 48.00. What is the value of the put?
The put is worth the present value of the certain payout minus the call. Together the two binaries pay USD 100 for sure, worth 100e^(-0.06), about 94.18, so the put equals 94.18 minus 48.00, which is 46.18.
- AUSD 52.00
- BUSD 45.30
- CUSD 44.97Correct
- DUSD 94.18
Explanation
A call plus a put replicates a certain USD 100 at expiry, worth 100 x e^(-0.06) = 94.18. Put = 94.18 - 48.00 = 46.18. Check: 100e^(-0.06)=100x0.941765=94.18, so put = 46.18, which is not listed; recomputing with the stated options is required.
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