CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
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 trades at 52, and the call costs 6.50. Using put-call parity, the price of the European put with the same exercise price and expiration is closest to:
The put price is about 2.57. Put-call parity says call plus present value of the exercise price equals put plus share. With PV of 50 at 4% equal to 48.08, put = 6.50 + 48.08 - 52 = 2.58, closest to 2.57.
- A2.57Correct
- B4.62
- C6.57
Explanation
Parity: c + X/(1+r) = p + S. PV of X = 50/1.04 = 48.077. Then p = 6.50 + 48.077 - 52 = 2.577, closest to 2.57 (about 2.58). Using the undiscounted X gives 4.50, and sign errors give other values.
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