CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
A non-dividend stock trades at 40. A six-month European call (strike 40) trades at 3.00 and the matching put trades at 2.50. The continuously compounded risk-free rate is 4% per year. The parity gap, measured as (c + PV of strike) minus (S + p), is closest to:
The present value of the strike is about 39.21, so call plus bond costs 42.21 against 42.50 for stock plus put. The gap is about -0.29, closest to -0.30, meaning the call side is underpriced.
- A-0.30
- B0.20Correct
- C0.70
Explanation
PV(X) = 40 x e^(-0.02) = 40 x 0.980199 = 39.208. c + PV(X) = 42.208. S + p = 42.50. Gap = 42.208 - 42.50 = -0.29, so the closest value is -0.30. The call-plus-bond side is cheap, so buy the call and bond, and sell stock and put.
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