CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
Which position most likely replicates a long European call on a non-dividend-paying stock under put-call parity?
A long call is replicated by buying the put, buying the stock and borrowing the present value of the strike, which is a short risk-free bond. This follows from rearranging put-call parity to call = put + stock - present value of strike.
- ALong put, short stock, long risk-free bond
- BLong put, long stock, short risk-free bondCorrect
- CShort put, long stock, long risk-free bond
Explanation
Parity: c = p + S - X/(1+r)^T. A call equals a long put, a long stock position and borrowing the present value of the strike (short bond). Option A is a synthetic put-type structure with the wrong signs on stock and bond, and option C shorts the put, giving the wrong exposure.
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