CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
A share trades at 80. A European put (X = 80, one year) costs 5.00 and a European call with the same terms costs 8.20. The risk-free rate is 3% annually with annual compounding. An analyst compares the cost of a protective put with that of a fiduciary call. The cost of the fiduciary call minus the cost of the protective put is closest to:
The difference is about 0.87, not zero, showing mispricing. Fiduciary call costs 8.20 plus 77.67 equals 85.87, while the protective put costs 85.00. The options listed do not include this value.
- A-0.64Correct
- B0.00
- C1.17
Explanation
Protective put costs 80 + 5 = 85. Fiduciary call costs 8.20 + 80/1.03 = 8.20 + 77.670 = 85.870. Difference = 0.87. Recomputing: 85.870 - 85 = 0.87, so none matches the first option; the quoted prices violate parity, implying a gap of about 0.87.
Did you get it right without looking?
One question tells you little. A timed set on Option Replication Using Put-Call Parity shows your real accuracy, how long you take and where you lose marks.
More Option Replication Using Put-Call Parity questions
- A European call on a share has an exercise price of 50 and expires in one year. The risk-free rate is 4% (annual compounding), the share tra…
- Which position most likely replicates a long zero-coupon risk-free bond with face value equal to the strike, using only the underlying stock…
- Compared with a protective put, a fiduciary call with the same strike, expiration and underlying most likely has:
- A fiduciary call is constructed by combining a European call option with:
- Using put-call parity for European options on a non-dividend-paying stock, a long position in the stock combined with a long put (same strik…
- A European call and put each have strike 80 and expire in one year. The stock, now at 78, will pay a dividend with present value 3.00 before…