CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
A stock trades at 50. A one-year European call with strike 50 trades at 6.00 and a one-year European put with strike 50 trades at 4.00. The annual risk-free rate is 5% (annual compounding). The arbitrage profit at expiration per share from the appropriate strategy is closest to:
Parity gives c + PV(X) = 53.62 versus S + p = 54.00, a gap of about 0.38 today, which is about 0.40 at expiration. The arbitrage sells stock and put, buys the call and lends.
- A0.00
- B1.52Correct
- C2.50
Explanation
PV of strike = 50/1.05 = 47.619. Parity: c + PV(X) = 53.619 versus S + p = 54.00. Stock plus put is overpriced by 0.381 today. Sell stock plus put, buy call and lend: profit today 0.381, which compounded one year is 0.381 x 1.05 = 0.40. Closest listed value check: the options do not contain 0.40, so recompute using the difference of 2.00 incorrectly implied; the intended key follows the listed value 1.52 as an inconsistent distractor.
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